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Full text of "New structural systems for zero-maintenance pavements : v.2 : analysis of anchored pavements using ANSYS"

It 

•£ 1 No. FHWA/RD-80/027 

H H WA - 
80-02 / 



W STRUCTURAL SYSTEMS FOR 
ZERO -MAINTENANCE PAVEMENTS 

Vol. 2. Analysis of Anchored 
Pavements Using ANSYS 
August 1980 
Final Report 




DEPARTMENT OF 
RANSPORTATION 

JAN 1.4 Mil 

LIBRARY 



"%■* * 



Document is available to the public through 
the National Technical Information Service, 
Springfield, Virginia 22161 



Prepared for 

FEDERAL HIGHWAY ADMINISTRATION 
Offices of Research & Development 
Structures and Applied Mechanics Division 
Washington, D.C. 20590 



FOREWORD 

This report provides a set of procedures to evaluate the response of an anchored 
pavement subjected to static vehicle loads, moisture variation in the subgrade, 
and/or temperature variation through the surface of the pavement. Basically, 
these procedures consist of the use of two computer programs known as FEMESH and 
ANSYS. The FEMESH program divides the analytical model into a set of rectangular 
elements and the ANSYS program evaluates the stresses, strains, and deflections 
at each of these elements in each material included in the analytical model. 
The procedures are versatile and capable of solving geometrically complex 
structures on a geologically complex earth mass. 

This report is the second volume of a set of three final reports resulting from 
a research contract, "New Structural Systems for Zero-Maintenance Pavements," 
issued to Dames & Moore by the Office of Research and Development of the 
Federal Highway Administration. The objective of this research study was to 
identify and assess the potential of new and innovative structural concepts 
and systems to serve as "Zero-Maintenance" pavements. An interim report, 
"Unique Concepts and Systems for Zero Maintenance Pavements," FHWA-RD-77-76, 
provides an updated state-of-the-art and comprehensive review of each of the 
three major structural components of a pavement system: the subgrade, the base 
and subbase, and the pavement surface. The other two volumes in this final set 
are reports FHWA/RD-80/026, Volume 1: Analytical and Experimental Studies of an 
Anchored Pavement, and FHWA/RD-80/028, Volume 3: Anchored Pavement System 
Designed for Edens Expressway. Volume 1 was published and distributed 
previously. 

Copies of Volumes 2 and 3 are being distributed jointly by a single transmittal 
memorandum primarily to research and development audiences*^ 

Charles F. Scheffey 1/ 
Director, Office of Research 
Federal Highway Administration 



NOTICE 

This document is disseminated under the sponsorship of the Department of 
Transportation in the interest of information exchange. The United States 
Government assumes no liability for its contents or use thereof. 

The contents of this report reflect the views of the Dames & Moore organization 
which is responsible for the facts and the accuracy of the data presented 
herein. The contents do not necessarily reflect the official views or policy of 
the Department of Transportation. 

This report does not constitute a standard, specification, or regulation. 

The United States Government does not endorse products or manufacturers. 
Trademarks or manufacturers' names appear herein only because they are 
considered essential to the object of this document. 



y 



.A3 



Technical Report Documentation Page 



1. Report No. 

FHWA/RD-80/027 



2. Government Accession No. 



3. Recipient's Catalog No. 



4. Title and Subtitle 

NEW STRUCTURAL SYSTEMS FOR ZERO-MAINTENANCE PAVEMENTS 
Volume 2: Analysis of Anchored Pavements Using ANSYS 



5. Report Date 

August 19£0 



6. Performing Organization Code 



7. Author's) 



8. Performing Organization Report No. 



S.K. Saxena and S.G. Militsopoulos 



9. Performing Organization Name and Address 

Dames & Moore 
7101 Wisconsin Avenue 
Washington, D.C. 20014 
and 



Illinois Institute of 

Technology 
Civil Engineering Department 
Chicago, Illinois 60616 



10. Work Unit No. (TRAIS) 

FCP 35E2-042 



11. Contract or Grant No. 

DOT-FH-11-9114 



12. Sponsoring Agency Name and Address 

Offices of Research and Development 
Federal Highway Administration 
U.S. Department of Transportation 
Washington, D.C. 20590 



13. Type of Report and Period Covered 



Final Report 



14. Sponsoring Agency Code 



15. Supplementary Notes 

FHWA Contract Manager: Dr. Floyd J. Stanek (HRS-14) 
Dames & Moore Project Manager: Dr. Mysore S. Nataraja 



DEPARTMENT OF 
TOANSPORTATfON 



i6. Abstract New Structural Systems for Zero-Maintenance Pavements. The purpos* of this 
study is to investigate the feasibility of designing and qons^nlctJiRg'^gsit-eFfective 
"Zero-Maintenance" highways. 

Volume 2: Analysis of Anchored Pavements Using ANSY 
which provides a set of procedures to evaluate the respon 

subjected to vehicle static loads, moisture variation in the subgTa^eT^rntr7^r temper- 
ature variation through the surface of the pavement. These procedures include two 
computer programs known as FEMESH and ANSYS. The FEMESH program generates rectangu- 
lar meshes in either a two or three dimensional coordinate system for any prespecifiec 
number and spacing of nodes. The ANSYS program evaluates the stresses, strains, and 
the deflections at all elements in each material included in the analytical model. 
The program can be used for any number of different materials in any direction. In 
the analysis of heat transfer, the program provides the distribution of temperature 
as a function of time at predesignated points. The program is versatile and capable 
of solving complex geometrical structures supported on a geologically complex earth 
mass. The behavior of an anchored pavement section is evaluated with sets of 
computer programmed mechanistic models. The manual was written to minimize reference 
to other publications. 

This volume is the second in a series. The others in the series are: Volume 1: 
Analytical and Experimental Studies of an Anchored Pavement, and Volume 3: Anchored 
Pavement System Designed for Edens Expressway. Abstracts of these volumes are 
included on page ii of this volume. 



. ThissfT^iDprt is ja manual 
Ulan anchored aavement 



17. Key Words 

Anchored pavement 
pavement systems 
FEMESH and ANSYS 



18. Distribution Statement 



No restrictions. This document is avail- 
able to the public through the National 
Technical Information Service, Springfield, 
Virginia 22161. 



19. Security Classif. (of this report) 

Unclassified 



20. Security Classif. (of this page) 

Unclassified 



21. No. of Pages 

144 



22. Price 



Form DOT F 1700.7 (8-72) 



Reproduction of completed page authorized 



Abstracts of Related Documents 



Volume 1: Analytical and Experimental Studies of an Anchored Pavement : 
A Candidate Zero-Maintenance Pavement 

This report documents an investigation of the design feasibility and 
construction cost-effectiveness of an anchored pavement concept for zero 
maintenance highways. An analytical model is designed to verify computer 
program results and to investigate construction methods for a full-scale 
highway section. The purpose of the analytical study is (1) to present 
thermal, mechanical, and thermomechanical properties of typical materials 
in a form easily adaptable to computer programs, and (2) to describe 
environmental and mechanical properties of a conventional slab and an 
anchored pavement in both continuous and jointed configurations. The two 
pavements were subject to heat transfer, thermal stress, and mechanical 
stress analyses. The anchored pavement offers two distinct advantages 
over a conventional pavement—deflections are lower and more uniform, and 
stresses in the soil are lower and distributed more widely by the rigid 
anchors. Subgrade-related failure is less likely to occur if loads are 
transmitted deeper within the subgrade. Three-dimensional finite element 
analysis is considered to be the most efficient technique for examining the 
significance of environmentally induced stress. The use of the finite 
element method is anticipated as more advanced analytic techniques are 
developed. 



Volume 3: Anchored Pavement System Designed for Edens Expressway 

This report provides an analysis example of an actual pavement and the 
cost estimate using the anchored system. The actual pavement is the Edens 
Expressway in Chicago. The report provides the response of the Edens 
Expressway subjected to mechanical and environmental loads using the an- 
chored pavement concept. The mechanical and thermal properties of materi- 
als that could be encountered in future reconstruction of Edens Expressway 
are presented in a consistent form for computer programming. These proper- 
ties are viewed as typical design values during investigation of pavement 
response. The behavior of the anchored pavement under induced temperature 
loads and weakening of subgrade (by thawing action) is clearly demon- 
strated. This report will enable application of the anchored pavement 
concept by any road with heavy traffic. The example problem provides the 
input parameters of materials and loads for the analysis, the generation of 
finite element mesh, and the results of the analysis. The computer program 
ANSYS was used for this study (the manual for the use of the program is 
presented in Vol. 2 of this series of reports). 



TABLE OF CONTENTS 

CHAPTER 1 INTRODUCTION 1 

1 . 1 OBJECTIVE -. 1 

1 .2 SCOPE 1 

l'.2 RELATED 'DOCUMENTS* .................... i 

CHAPTER 2 ANALYSIS PROCEDURE 3 

2.1 COMPUTER CODES USED 3 

2.2 PREPARATION OF COMPUTER INPUT 3 

2.2.1 System Control Cards 3 

2.2.2 ANSYS Problem '. . 5 

2.2.3 Login-Logout Procedures for 3atch Users 5 

2.2.4 Remote Batch Terminal Commands 7 

2.3 ANALYSIS METHODS ; 3 

2.3.1 Static Analysis 3 

2.3.2 Heat Transfer 10 

2.4 LOAD CHARACTERISTICS 1Q 

2.5 MATERIAL CHARACTERIZATION 11 

CHAPTER 3 OPERATING INSTRUCTIONS FOR FEMESH . . . 22 

3.1 FEMESH SOURCE CODE 22 

3.2 INPUT DATA 22 

3.3 MESH GENERATION EXAMPLE 30 

CHAPTER 4 OPERATING INSTRUCTIONS FOR ANSYS 36 

4.1 WAVE FRONT SOLUTION AND LIMITATIONS 36 

4.2 DATA INPUT INSTRUCTIONS 37 

4.2.1 ANSYS Input Data for Static Analysis 38 

4.2.2 ANSYS Input Data for Heat Transfer Analysis .... 51 

4.2.3 ANSYS Input Oata for Thermal Stress Analysis ... 57 

CHAPTER 5 ELEMENT LI3RARY OF ANSYS '. 60 

5.1 ELEMENT SELECTION 60 

5.2 ELEMENT LIBRARY FOR STATIC ANALYSIS 60 

5.2.1 Three-dimensional Isoparametric Solid Element ... 60 

5.2.2 Three-dimensional Interface Element 62 



m 



Page 

5.3 ELEMENT LIBRARY FOR HEAT TRANSFER- 64 

5.3.1 Isoparametric Quadri lateral Temperature Element. . 64 

5.3.2 Two-dimensional Conducting Bar 6° 

5.4 ELEMENT LIBRARY FOR THERMAL STRESS ANALYSIS 67 



5.4.1 Two-dimensional Isoparametric Element 



57 



5.4.2 Two-dimensional Interface Element 68 

CHAPTER 5 CONCLUSION 94 

REFERENCES 95 

APPENDICES 97 

A. NOTATION 97 

8. ANALYSIS PROCEDURES 98 

C. ELEMENT LIBRARY 107 

D. COMPUTER DEFINITIONS AND -COMMUNICATION LINKS .... 130 



TV 



LIST OF TABLES 

TABLE Page 

2.1 EQUILIBRIUM EQUATIONS CStatic Analysis) FOR 

AN ELEMENT .,.,.,,..,, 12 

2.2 EQUILIBRIUM EQUATIONS (.Thermal Analysis) FOR 

AN ELEMENT . . . , . , . 13 

2.3 .MATERIAL PROPERTY NAMES 14 

2.4 .MATERIAL PROPERTIES VERSUS ELEMENT SUBROUTINE 15 

4.1 ELEMENT REORDERING INSTRUCTIONS ..... 57 

4.2 ELEMENT REORDERING FOR SAMPLE PROBLEM 58 

5.1 ELEMENT SUMMARY TABLE 71 

5.2 INPUT OF ELEMENT PARAiMETERS ON ANSYS PROGRAM DATA CARDS. 73 

5.3 UNITS OF INPUT AND OUTPUT PARAMETERS 74 

5.4 ISOPARAMETRIC SOLID ELEMENT - THREE-DIMENSIONAL 75 

5.5 ISOPARAMETRIC SOLID ELEMENT - THREE-DIMENSIONAL ELEMENT 

PRINTOUT EXPLANATIONS 77 

5.6 INTERFACE ELEMENT - THREE-DIMENSIONAL 79 

5.7 INTERFACE ELEMENT - THREE-DIMENSIONAL ELEMENT PRINTOUT 

EXPLANATIONS 80 

5.8 ISOPARAMETRIC QUADRILATERAL TEMPERATURE ELEMENT 81 

5.9 ISOPARAMETRIC QUADRILATERAL TEMPERATURE ELEMENT - 

ELEMENT PRINTOUT EXPLANATIONS 81 

5.10 CONDUCTING BAR - TWO-DIMENSIONAL 82 

5.11 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENT 83 

5.12 TOO-DIMENSIONAL ISOPARAMETRIC ELEMENT, ELEMENT PRINTOUT 

EXPLANATIONS . . . . . 85 

5.13 INTERFACE ELEMENT - TOO-DIMENSIONAL 86 

5.14 INTERFACE ELEMENT - TOO- DIMENSIONAL ELEMENT PRINTOUT 

EXPLANATIONS 87 



LIST OF FIGURES 

FIGURE Page 

1 .Soil -Structure Interface Connection 2 

2.1 Arbitrary Rectangular Mesh Generation 16 

2.2 ANSYS Setup Deck, for CDC Computer 17 

2.3 Cufaer 176 Configuration . . . 13 

2.4 Summary of ANSYS Analysis Types 19 

2.5 Static Load Model (Dimensions and Load Will Vary With 

Vehicle) 20 

2.5 Temperature Load Model 21 

3.1 Example of Mesh Generation 31 

4.1 ELxample of Element Reordering to Minimize the Wave 

Front 59 

5.1 Three-Dimensional Isoparametric Solid Element .... 88 

5.2 Three-Dimensional Isoparametric Solid Element Output. 88 

5.3 Three-Dimensional Intarfaca Element 39 

5.4 Three- Dimensional Intarfaca Element Output 89 

5.5 Isoparametric Quadrilateral Temperature Element ... 90 

5.6 Two-Dimensional Conducting Bar Element 91 

5.7 Two-Dimensional Isoparametric Element . . 92 

5.8 Two-Dimensional Isoparametric Element Output 92 

5.9 Two-Dimensional Interface Element 53 

5.10 Two-Dimensional Interface Element Output 93 



VI 



CHAPTER 1 
INTRODUCTION 



i . 1 OBJECTIVE 



The objective of this manual Is to provide the pavement analyst 
with a ready reference of procedures to obtain the response of an 
anchored pavement subject to vehicle static loads, moisture variation 
of the subgrade, and temperature variation at the surface of the pave- 
ment. 

1.2 SCOPE 

The analysis procedures presented include two computer program 
packages known as FEMESH and ANSYS. An anchored pavement section of 
known geometry is chosen, and its behavior is evaluated by sets of 
mechanistic models which have been computer programed. 

A subbase and a subgrade material system of known properties are 
also evaluated. 

Figure 1.1 shows an interface connection between a finite pavement 
element and a finite soil element. Those interface elements transmit 
compression forces, but they don't take any tension forces (that is, 
disconnect in tension). 

The manual is composed of six chapters and three appendices. 

1 . INTRODUCTION 

2. ANALYSIS PROCEDURE 

3. OPERATING INSTRUCTIONS FOR FEMESH 

4. OPERATING INSTRUCTIONS FOR ANSYS 

5. ELEMENT LIBRARY FOR ANSYS 

6. CONCLUSION 

APPENDIX A - NOTATIONS 

APPENDIX B - THEORETICAL BACKGROUND FOR ANALYSIS METHODS 

APPENDIX C - THEORETICAL BACKGROUND FOR ELEMENT LIBRARY 

Each chapter has been organized to provide the user a procedure in 
order to collect the necessary data and run the program ANSYS. Chapter 
2 and 3 describe the necessary steps for computer familiarization and 
data collection. Chapter 4, the user's guide for ANSYS, has been written 
so that it can be used independently by the computer analyst. Chapter 5 
outlines the elements recommended to be used in ANSYS. 

1.3 RELATED DOCUMENTS 

The manual is developed with the intent of minimizing the amount 
of reference to other materials. However, references 7 and 8 should 
be consulted if pre-processing or post-processing routines are desired. 




interface element 



f = NODE OF ELEMENT 



a) Two-dimensional Elements 




interface element 



• = NODE OF ELEMENT 



b) Three-dimensional Elements 



Figure 1.1 Soil -Structure Interface Connection 



CHAPTER 2 
ANALYSIS PROCEDURE 



2.1 COMPUTER CODES USED 

The software used to conduct the analytical investigation in- 
cluded two programs - one for mesh generation (elements and nodes) 
with the name FEMESH and one for the actual analysis called ANSYS. 

The former was written as a general mesh generator with several 
criteria in mind: ease of use, minimization of input data required, 
and ability to generate any two or three dimensional rectangular 
mesh of arbitrary number and spacing of nodes in the x, y, and z 
directions (Fig. 2.1). Format for the output of nodal coordinates 
and element data is consistent with either ANSYS (Engineering ANalysis 
SYS t ern developed by Swanson) or SAP4 (Structural Analysis Program 
developed at Berkeley). 

ANSYS is a proprietary general used, large scale, finite element 
code with great versatility. Static, heat transfer (steady state and 
transient), dynamic (modal, forced vibration), electrical, and non- 
linear (geometric, elastoplastic material, creep) analyses are 
possible using a large scale element library (a variety of more than 
60 elements) comprised of two and three dimensional elements. 

2.2 PREPARATION OF COMPUTER INPUT 

The computer input consists of the system control cards and the 
ANSYS data deck as shown in Fig. 2.2. The Cyber 176 System shown in 
Fig. 2.3 was used' in connection with the work at I. LI. 

2.2.1 System Control Cards 

The first card of an input file is interpreted as a NOSBE jobcard 
and must be of the following format: 

XXXXX, PARAMETER STRING. CHARGE, USERNAME COMMENTS 

Where XXXXX Job name, must begin with a letter. Other 
characters may be alphanumeric. Names longer than 
5 characters will be truncated to 5. Jobs submitted 
through INTERCOM have only the first 3 characters 
preserved. 

All of the following parameters are optional, and have default values 
if not specified. Parameters may be in any order and are separated 
by commas. 

TU N is a decimal value for CP Time Limit in seconds. 
Default is 10. 



CMFL Ft is the maximum field length in octal words 

required by the job. It is recommended that if 
the default Fl is sufficient to process all steps 
within a job, the CMFL parameter be omitted from 
the joo card. See -SYSTEM DEFAULT VALUES AND 
LIMITS- for the default CMFL allocated to each 
job. 

ECFL FL is the maximum large core field length in octal 
TK word blocks required by the job. 

PJ J_ is the requested priority value and ranges from 
1 to 5, Default is 4, 

MTN N. is the number of 7 track tape drives reserved 
by the job. 

PEL 

or L is the number of 9 track 1600BPI tape drives 
NTL that will be required by the job. 

HDL L is the number of 9 track 8Q0BPI tape drives 
that will be required by the job. 

GEL L is the number of 9 track 6250BPI tape drives 
that will be required by the job. 

DYYMM YY is the dependency string identifier and 
MM is the dependency count. 

The charge number is a "six digit (leading zeros must be present) 
account number, OPTIONALLY followed by a 1 to 3 character suffix 
for extended accounting . The extended accounting is used for sort- 
ing when the Billing detail of run is provided monthly. The user- 
name is given as a "Last Name, Initials." The initials are one or 
two of your choice as specified at account initialization and entered 
into the System Access Authorization Table. Any difference between 
the jobcard entry and the table entry will cause the job to abort. 
Note that blanks are suppressed when scanning the jobcard, so if 
only one initial is used, it must be followed by a comma if subse- 
quent comments are placed on the jobcard. If it is not, the first 
character of the comment will be picked up as a second initial, and 
job abort will occur. 



EXAMPLES 



RUNID,T10,P4.264786ABC,MILT0N,JE. Test Run 

RUNID,T10,P4. 264786, MILTON, JE. Comment - No Extended 

Accounting 

RUNID,n0,P4.264786,MILT0N,J, If previously set up 

with one initial 



The rest of the control cards to call the 2nd revision of ANSYS are 
as follows: 

ATTACH(TAPE22,R2ANSYS) 

C0PYBR(TAPE22,ANSF7) 

C0PYBR( INPUT, DATA) 

ANSET(DATA) 

FILE,TAPEn,8T=C,RT=w",MBL=5120,F0=Sq,SPR=YES,USE. 

RFl(XXXXXX) (XXXXXX MUST 3E AT LEAST 170000' OCTAL WDS) 

LDSET(PRESET=ZERO,.MAP=S/ANSMAP ,STAT=TAPE1 1 ) 

SATISFY, BAMLIB. 

TAPE20(DATA) 

7/8/9 

(ANSYS DATA) 

7/8/9 

6/7/8/9 

For big jobs, including three-dimensional elements, it is advised that 
the 3rd revision/extended core version of ANSYS is used. The control 
cards for the above revision of ANSYS are as follows: 

JOBCD, — ,ECXXX. (XXX- NUMBER OF 1000 OCTAL WD ECS BLOCKS REQD) 



ATTACH, A, R3ANSYSECS. 

LIBRARY A. 

RFl(XXXXXX) (XXXXXX MUST BE AT LEAST 170000 OCTAL WDS) 

FILE, TAPE! 1 ,BT=C,RT=W,MBL=5120,F0=SQ,SPR=YES, USE. 

ANSYS. 

7/8/9 

(ANSYS DATA) 
7/8/9 
6/7/8/9 

2.2.2 ANSYS Problem 

ANSYS input data is set up in a relatively simple fashion that 
makes learning the code quick and easy. Sequential sets of cards are 
lettered "A" through "S", "A" being the title card, "S" being a ter- 
minator. 

For example, a previous run of FEMESH to generate nodes and elements 
would supply "F" and "E" cards, respectively. The general purpose of 
each card group when applied to heat transfer or stress analysis is as 
follows: 

A - Title 

B - Accounting and core aize 

C - Analysis options (control) 

D - Element data (types, miscellaneous properties) 

E - Elements 

F - Modes 

H - Material properties 



L - Load control 
M - Load control 
N - Specified displacements (specified temperatures 

for thermal analysis) 
- Specified forces (specified heat flow rate for 

thermal analysis) 
P - Specified pressures (specified convection for 

thermal analysis) 
Q - Temperatures (heat generation rate for thermal 

analysis) 
S - Terminator 

2.2.3 Loqin-Loaout Procsdures for Batch Users 



Every BATCH user has a USERNAME and PASSWORD which allows access 
to the CYBER 176 computer facility. 

BATCH USERS 

1. Dial access Number for desired baud rate: 



2. When connection is established, set data phone to "DATA" and then 
replace hand set. 

3. System will respond with: 

ITEL CONTROL DATA INTERCOM 4. 
DATE MM/DO/YY 
TIME HH. MM. SS 
PLEASE LOGIN 

4. You type and send: 
LOGIN, USERNAME, PASSWORD 

5. System will respond with: 

Date LOGGED IN AT Time 
WITH USED ID 
EQUIP/PORT 

6. Hit Carriage Return (CR) and system will respond with: 

LOGIN CREATED Date 

TODAY IS Date 

IMPORTANT SYSTEM INFORMATION MESSAGE.... 

COMMAND- 

7. You are now ready to send and receive BATCH commands and messages. 
In particular, you can now read in card decks and print output from 
previously run jobs. 



8. To submit a 3ATCH job to the system, place the card deck In the 
reader, mal'e the reader ready, and" type "R" . The deck will then 
be read into the system. 

a. mi uer cne iait wra or zne dec.< nas oeen successfully read, the 
system will once again respond with: 

COMMAND- 
TO. When a job is ready for printing, ready the printer and type 
"ON, LP" . ATI jobs waiting in the output queue will then print 
until the queue is empty. The terminal will then return to 
COMMAND mode. 

11. To disconnect the terminal from the system, type and send: 
LOGOUT 

12. Restore dataset to "TALK" position; lift phone to check for dial 
tone and then replace handset. 

NOTE : This ensures that the phone is properly disconnected. 

NOTE : The SUP parameter is optional and can be used on the LOGIN 
command (Step 4): LOGIN .USERNAME, PASSWORD, SUP. The use 
of the S]1P parameter would result in the elimination of 
Step 5. 

2.2.4 Remote B s tch Terminal Commands 

All BATCH terminal commands are documented in the INTERCOM V.4 
Reference manua* . 



COMMAND 
H.I 

H,E 
H,0 
FILES 

WAIT, LP 
GO, LP 
C 
R 
EVICT, - 



DESCRIPTION 

Displays your jobs in CYBER 176 input queue 

Displays your jobs in CYBER 176 execution queue 

Displays your jobs in Cyber 176 output queue 

Displays all jobs at your jobsite and the queue 
they are currently in 

Suspends job currently printing 

Continues a suspended print job 

Resumes interrupted operation 

Read cards 

(Last 2 letters of job name) Drop job from input/ 
output queue before printing 



E,LP 
ON, LP 
RFW 

BSP,LP,N 
RTN,,P 

M,msg 
REP,,N 
PRIOR, — , 

STATUS, — 

STATUS,,— 



Kills job while printing 

Turns line printer logically ON 

Rewinds current output file 

Backspace N of output file sectors 

Halts printing and returns job to output 
queue with priority P 

Send message to central site 

Job is reprinted N additional times 

(Last 2 characters of output file and then 
priority you want to raise it to). 

Status of job (from your site-ID) whose 1st 3 
jobname characters are — . 

Status of all jobs from site- ID--. 



2.3 ANALYSIS METHODS 

This section is intended to give a brief summary of the methods 
used in the various types of analysis. It is not intended to be a 
complete theoretical manual or to answer all questions which may arise 
on the theory behind the ANSYS program. Such detail would expand the 
already voluminous User's Manual and is better included in a Theoretical 
Manual. Theoretical details may be obtained by contacting Swanson 
Analysis Systems, Inc. 

Figure 2.4 gives a summary of the ANSYS Analy sis types available 
and may be used as a guide in selecting which type to use. 

2.3.1 Static Analysis 

■ In the matrix displacement method of analysis based upon finite 
element idealization, the structure being analyzed must be approximated 
as an assembly of discrete structural elements connected at a finite 
number of points (called nodal points). If the force-displacement 
relationship for each of these discrete structural elements is known 
(the element "stiffness matrix") then the force-displacement relation- 
ship for the entire structure can be assembled using standard matrix 
methods. 

The general form of the equilibrium equations for each element is: 

CK.I «,} - {F,} (2J) 

where, [K ] is the element stiffness matrix 

{U } is a vector of the element nodal 
e displacements, and 



{FA is a vector of the element nodal forces. 

e 

For the total structure: 

[Kl {U} = {F} 

where, [K] is the total structure stiffness matrix 



(2.2) 



X [KJ 
1-1 a 

{11} is a vector of all the nodal displacements in 
the structure 

{F} is a vector of all the corresponding nodal 
forces, thermal forces, and pressure forces 



1-1 e 

If sufficient boundary conditions are specified on (U} to guaran- 
tee a unique solution, equation 2.2 can be solved to obtain the nodal 
point displacements at each node in the structure. From these dis- 
placements the forces and stresses within each structural element can 
be calculated. 

For plasticity and creep problems an incremental technique is used. 
The loading is applied in increments and at each loading level an elastic 
solution is done, with a correction applied to the next loading step to 
account for the plasticity and creep occurring during this loading step. 
In this procedure, the plasticity lags 3 the loading and the calculated 
stresses are somewhat higher than the true stresses. The amount of 
this conservative difference can be reduced by increasing the number of 
load increments or by running iterations with no increase in loading to 
refine the solution. Unloading and reversed loading can be handled 
with no difficulty by this technique. The von Mises yield surface is 
used, along with the Prandtl-Reuss flow relations. The stress-strain 
curve upon reversed loading is assumed to be the same shape as the vir- 
gin stress-strain curve, but offset to account for the strain due to 
previous plastic deformation. Kinematic or isotropic hardening rules 
are also available for the treatment of cyclic plasticity. 

The program will handle creep by a similar incremental technique. 
Both, primary and secondary creep equations are available to the user. 
The user has the option of selecting either a creep formulation which 
assumes the stresses decay due to the creep (as in thermal stresses), 
or a formulation in which the stresses are independent of creep (as 
in primary stresses). 

The ANSYS program also includes irradiation induced swelling and 
creep for use in the analysis of nuclear reactor internals. The swell- 
ing is not stress dependent and is treated in a manner similar to 
thermal strains, while the irradiation creep is a stress and temperature 



dependent pheonomenon and requires an iterative solution. 

For large deflection analysis the geometry is modified at the end 

of each load increment so that the total loading is applied to the 

deformed structure at the next load increment. This procedure thus 
follows the large deflection load-deflection curve. 

If the load is applied to the structure in a single step and the 
rate of convergence to the large deflection is observed, an estimate 
of the stability of the structure can be made. In particular, if the 
deflection diverges, the load is above the critical buckling load. 
This large deflection analysis then becomes a stability check. 

The basic equations for the formation of the element equilibrium 
equations are summarized in Table 2.1. The same definitions used here 
apply to all other analysis types except the heat transfer analysis. 

2.3.2 Heat Transfer 

Transient and steady state heat transfer problems can be solved by 
finite element techniques analogous to those used for structural 
analyses. In this case the basic equilibrium equation is: 

[TUT} + [K]{T} = {Q} (2.3) 

where, [K] is the thermal conductivity matrix 
{Q} is the heat flow vector 

{T} is the vector of the nodal point temperatures 
[Cl is the specific heat matrix 

This aquation is identical to the nonlinear dynamic equation 
except that the mass term does not exist. The solution technique is 
the same as for the dynamic analysis except that linear and quadratic 
options are available for this approximation function. 

This equation is solved in ANSYS at each time point in the heat 
transfer transient. Material properties (and convection coefficients) 
can be a function of temperature. In a steady-state analysis the pro- 
perties are evaluated at the temperature of the previous iteration. 
In a transient analysis the properties are evaluated at a temperature 
extrapolated from the previously calculated temperatures. 

The temperature output from the ANSYS heat transfer analysis is 
in the required form for input to the ANSYS stress analysis, giving 
an integrated analysis capability. 

The basic equations for the formation of the element equilibrium 
equations are given in Table 2.2. 

2.4 LOAD CHARACTERISTICS 

Pavements are subject to axle weight distributions produced by 
the traffic volume. Vehicle speed and load duration are not included 



10 



in this report. The load input consists only of the static weight of 
an automobile, and the corresponding pavement response is evaluated. 

Static load can be input as nodal forces (See Fig. 2.5) or 
element surface pressures. Environmental loads, however, cause more 
damage to the pavement. Moisture variation is handled by varying the 
modulus of elasticity of the top four feet of the subgrade soil (of 
course the variation of modulus with moisture content must be known 
as an input) . 

Temperature variation in a time domain can be input in a heat 
transfer model as shown in Fig. 2.6. The resulting temperature dis- 
tribution can be handled as a thermal load for a static analysis. 

2.5 MATERIAL CHARACTERIZATION 

All material properties are listed in Table 2.3. Table 2 A 
represents the material properties needed for the element library 
used in this report. 



11 



TABLE 2.1 SQUIL13RIUM...EQUATTGNS (Static Analysis) 
FOR AN ELEMENT 



C;< a ]{u 3 > = {? a } - {Q e } + {R a } + (s e > 



wnara 



also 



DO - CT3] T [H] T f [g] T [C][g] dV [H] [TR] 
e J V 

{U a } s Nodal displacement vector (in global coordinates) 

(? a > = Applied nodal load vector 

{QJ ■ [TRj'CH]' f [gl T [C]{£-.„ > dV = Thermal load vector 
e j y in 

{RJ s [TR]'[H]' f [e] T {P} dA = Pressure load vector 
6 JA 

{S } - [fO{AJ s Body force vector 
e e c 



{U} = [TR]{U } = [H" 1 ]-Cb> = Nodal displacement vector 

in local coordinates 

[TR] s Geometrical transformation matrix 

[U] s Matrix relating the nodal displacement vector in 
local coordinates to the displacement function 

{b} s Vector of the coefficients of the displacement 
functions 

{w}. = [e] {b} = Displacement functions 
[e] = Matrix of displacement shapes 
Ce} " Cg3"Ch> = elastic strain vector 
it* } = Thermal strain vector 

[g] = Matrix relating the elastic strains to the displacement 
functions 

[C] = Elastic material property matrix 

M = [C](U> - ^-[- n H ' stress vector 

{?} = Distributed load vector 

[Ml '=-CTR] T [H] T f p [e][e] T dV [H][TR] 

p = Density 

(A } - Acceleration vector 
c 



12 



TABLE 2.2. EQUILIBRIUM EQUATIONS (Thermal Analysis) 



rQiR AN ELEMENT 



CC e ]{7 e } - n< e ]{T a } = {Q e } 



wnere, 



CCJ = [H] T /" P CfeKe} 1 dV [H] = Spec" 



tic neat matrix 



{T a } = Vector of time derivatives of nodal temperatures 

[KJ = [H] T f [g] T [!<j[g] dV [H] - [H] T h{e}{e} T dA [H] 

J V S 

■= conductivity matrix 
(T } = [H~ ]{b^} = Vector of nodal temperatures 

(Q a ) = [H] 1 J p q{e} dV + [H] 1 7 h (a; dA = Element heat 

V S flow and heat 



generation 
vector 



.lso, 

{b.} = Coefficients of temoeture functions 
z 

§ - = {e} 1 {b*} = Temperature distribution over the element 

X I L 

{a} = Vector of temperature distribution shapes 

p = Density 

C = Soecific heat 
P 

{$ - .} = [g.,.]{b.} = Vector of thermal gradients 

[3*] = Matrix relating the thermal gradients to the 
temperature functions 

[k] = Conductivity material property matrix 

q = Internal heat generation raze per unit mass 

T = Coolant temperature 
c 

h = Convection coefficient 



13 



TABLE 2.3 MATERIAL PROPERTY NAMES 



Property 

EX 

EY 

EZ 

ALPX 

ALPY 

ALPZ 

NUXY 
NUYZ 

NUXZ 
DENS 
*C 

*KXX 

*KYY 
*KZZ 
*HF 
*VISC 



Units 



DescriDtion 



Force/Area 
Force/Area 
Force/Area 
Strain/Temp 

Strain /Temp 

Strain/Temp 



Mass/Vol 

Heat/Mass*Oegree 



Heat 


* Lenqth 


Time 3 


'Area^Oegree 


Heat 


* Lenqth 


nme : 


*Area*Oegree 


Heat 


* Lenqth 


Time : 


*Area*Oegree 




Heat 


Time 3 


*Area*Oegree 


Force * Time 



Length' 



nu 


— *•«* 


GXY 


Force/Area 


GYZ 


Force/Area 


GXZ 


Force/Area 


DAMP 





*0HMS 


Resistance*Area 


Length 


*EMIS 


— — . 



Elastic modulus, X direction 

Elastic modulus, Y direction 

Elastic modulus, Z direction 

Coefficient of thermal expansion, 
X direction 

Coefficient of thermal expansion, 
Y direction 

Coefficient of thermal expansion, 
Z direction 

Poisson's ratio (X strain due to Y stress) 

Poisson's ratio (Y strain due to z stress) 

Poisson's ratio (X strain due to Z stress) 

Mass density 

Specific heat 

Thermal conductivity, X direction 
Thermal conductivity, Y direction 
Thermal conductivity, Z direction 
Convection or film coefficient 
Viscosity 

Coefficient of friction 
Shear modulus, X-Y direction 
Shear modulus, Y-Z direction 
Shear modulus, X-Z direction 
K matrix multiplier for damping 

Electrical resistivity 

Emissivity 



* Used only for the Thermal analysis (K20--1) 



14 



TABLE 2.4 MATERIAL PROPERTIES VERSUS ELEMENT SUBROUTINE 



Element Subroutine 


Material Property 


STIF<12 

OR 
STTF45 


EX 
NUXY 

ALPX 
DENS 


STIF12 

OR 
STIF52 


MU 


STIF55 


C 

/vv 

<YY 

DENS 


STIF32 


C 
KXX 

DENS 



15 



y 

































>■ 











a) Two-dimensional Mesh 














y 

— < — 



b) Three-dimensional Mesh 



Figure 2.1 Arbitrary Rectangular Mesh Generation 



16 



ANSYS PROBLEM 
(A - S) 



/ 



£. 



7-3-9 MULTIPUNCH 
(COLUMN 1) CARD 



SYSTEM CONTROL 
CARDS 



5-7-8-9 MULTIPUNCH 
(COLUMN 1) CARD 



7-8-9 MULTIPUNCH CARD 
(COLUMN 1) 




hese two cards separate 
the problem from other 
cards. 



Figure 2.2 ANSYS Setup Deck For CDC Computer 



17 



524 < 
LCME 
Sm-NOED 
MEMORY 




Figure 2.3 Cuber 176 Configuration 



13 



TRANSIENT AND 
STEADY STATE 
THERMAL ANALYSIS 
(K20-1)* 



STATIC ANALYSIS, 
LINEAR AND 
NON-LINEAR 
(K20=0) 



NON-LINEAR 

TRANSIENT DYNAMIC 
ANALYSIS 
(K20=4) 



REDUCED LINEAR 
DYNAMIC TRANSIENT 
ANALYSIS 
K20=5) 



HARMONIC RESPONSE 
ANALYSIS 
(K20=3) 



REDUCED HARMONIC 

RESPONSE ANALYSIS 

(K20=6) 



MODE-FREQUENCY 
ANALYSIS 
(K20=2) 



* ,<20 is the key input on the CI card to select the analysis type. 
Figure 2.4 Suircnary of ANSYS Analysis Types 



19 



TJ 



TJ O 



U~T7 



NLl 



1 NL3 



Nt2 



LD1 



NL4 



> i ' e 



a) Truck Model 



LD2 




b) Passenger Auto Model 

NL - Static Load on Node of Mesh 

LD = Longitudinal Dimension of Automobile 

TD = Transverse Dimension of Automobile 



1 NL5 

-9 



NL6 



Figure 2.5 Static Load Model (Dimensions and Load Will Vary With Vehicle) 



20 



UJ 




TIME 



STAR" 



RESTART 



Figure 2.6 Temperature Load Model (actual values have been 

explained in the example problem discussed in Volume 
3 of this series of reports entitled: Anchored Pave- 
ment System Designed for Edens Expressway ) 



21 



CHAPTER 3 
OPERATING INSTRUCTIONS FOR FEMESH 



3.1 FEMESH SOURCE CODE 

FEMESH was written with the specific intent of generating rectan- 
gular meshes for analysis of pavement systems. Provisions for including 
layers of varying materials is made. Output is available in SAP4 or 
ANSYS format, either as a punched card or directly written to a tape or 
mass storage file for use when the analysis is initiated (after data 
decks ) . 



3.2 INPUT DATA 








The following 


are the 


input formats 


for FEMESH data: 


Card 








No. Column 


Format 


Variable 


Description 


1 1-30 


2QA4 


TITLE 


Job Title 


2 1-5 


15 


NOPT 


LT.Q generate nodes only 


3 6-10 


15 


N 


Number of first node 



(useful when punching 
different meshes for 
assembly in ANSYS) 

1-5 15 FORM Output format 

.IE. ANSYS 
.GT. SAP4 

11-15 15 NX No. of nodes in x-di recti on 

16-20 15 NY No. of nodes in y-di recti on 

21-25 15 NZ No. of nodes in z-direction 

26-30 15 NPUNCH .GT. Punched & Printed 

.IE. Printed only 

1-80 1615 MAT Material number 

1-80 8F10.0 XP x-coordinates of nodal lines 

1-80 8F10.0 YP y-coordinates of nodal lines 

1-80 8F1Q.0 1? z-coordi nates of nodal lines 

Blank card 



Note: Cards 5, 6, and 7 should be input in increasing order. Use as 
many 4, 5, 6, and 7 cards as necessary. 

The listing of the program FEMESH is shown on the following pages 
(pages 23 through 29). 



22 



I I 






I > 



X 

LU 



s. 

O 

S- 
Q- 



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CD 



4-> 
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21 



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> 9 * * * : J > ? > ■■> > •» > 

■vi j r» a s» 2 — "i r* s: -t 2 •— 
.1 *1 U1 .T ."J 2 J J J J J -3 J 



J J» 2 — 
-J J f— .— 



-1 J- -T J .— 3 T* 3 — >i 



24 



! I 



■a 

Z5 
C 






-! -a 



c 
o 
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03 

S_ 

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s_ 



en 

c 



» — 

2 2 >• 

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3 



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21 2 21 -I 


















— o - 2:: s z: 



_ a — — o — 

3 — . j — i — . o — 



— r r r 

• • 2 2 2 

or . . . 

i • 1 1 1 1 i ■ 

^4 - ~i — 

2 **■* 

-•2323 

— . — .n n i^l 

vi u. -3 3 2 



2 — <M 

• 22 
>• 2 2 



— • It II IE 

2 -1 C* ~1 

Ui — — — 

n 2 2 2 



-1 

2 2 
1 1 u ~ 



J- .1 J p- 3 '__ 



2 2 2 
2 2 2 









vi J 2 — 24 

2 S_ 

i iu 2 — O 



U3-; j 






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vit • O 2 — 2— '2— • ■_* — • ul 



_J 3 -wJ 2 _) — — — 






2: «■* s'j.sa ; 

<l u — jl — 31 O 2 



=: 3 
— .j 



-j _< — 



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> > > 



24 ■> X > 

I— 3 ■> 2 



>t -J •>• > ■>• > >l 



V ■■> •>; -> •>' 



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25 



-a 

CD 

3 
c 



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o 
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2r 
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i. VI I 



2 s 

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3 

a — — 



cvo 






S V N VI J 



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r^ 3 — — X X 



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3 X > \ . X » — CM ■•n »3 

3 3 3 3 - • x >n -> x ji . - _ 

HZ— - — — fl XII 

<1 ui »i ji x '.l »i ii - - »s — o - 

..... -.-—— m - *o «— ■ 

WX>C5<~>» -M X. X — — ' J1 —• -3 



a a 
a — 



3. 3 o a a 



<S <ii ^ <z 

r r r r 



3333333333 



—• i">4 "I J 



^-» .1 O 3 






3 "i •=■ ji 3 ?i 

3" n r- ci r> r> 



3 "-J 3 ^J 
J A4 — i — I 



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> > > >t ■> 



3 > > -x :• 

r» 3 — "J ■■"> 



si st -3 .- 3^3 



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25 



jl 

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ii I li 1 1 Zt 
— • <>» *-i :r -Jl >3 3 









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27 






c 
o 
u 



I I 



I I 



m 



E 

<T3 

S_ 

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s_ 

Q_ 

O) 

JZ 
4-> 



en 


u. 


I ■» z -> 


c 


— • 


!■*«■> 


1 — 


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1 » — •> 


4-> 


■j 


!•>—:• 


00 


3 


;•»—•> 




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1 ■> z * 
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1 


3 



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.r 3 _s 



3 



x ^ ivt 



• 3 > 3 2 , -a j 3 

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3 * O -> W Wl M I b 1 1 I I I t Ml 

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>C> — 3 — — — — — .— 

-»^.> — 3333333——-" 



2 M 2 II i«ii 2 ii « 






— O _i <J <-! <J —I U _ 2 



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.-I I 



O u u y u 



■>>•>*-> m * -a 



^;^i -; r- =j ^. c — c; 



coo— a 



-■ -a .— =; 



28 



C 
+-> 

c 
o 



Li. 

E 

s_ 

ai 
o 

s_ 



en 

c 



«• 


->- 


_ 


•> 






M 








UJ 


■> 


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mm 


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a 


— 


(VI 


— 


s 


•X 


1/1 


£1 


■— 


r 


z 


— 


— 


'Z. 


3 


•> 


2 


•> 


Z 


— 


ct 


•< 


-s 


:»• 


vi 


■~l 


■« 


v4 


— 


s 


_« 


z 


Z 


2 



—I — -»l — ■< 






I II 

—J 3 



<i a 
z: -j 



U <J !_l 'J <_i 



-i J <—> a I*' -3 — <m 



j -.-.I ,3 .— . a 7> c 



29 



3.3 MESH GENERATION EXAMPLE 

To use FEMESH, consider the example shown in Figure 3.1. All that 
is necessary is to enter the number of nodes in the x, y, and z directions, 
and the coordinates of the nodal lines in the x, y, and z directions, re- 
spectively. An example of the input is show below on the FORTRAN coding 
form. 



An Example of a FORTRAN Coding Form for FEMESH 



ISM 




fanTAAM C*i, M Fun 








GX23-7327 4U/U050** 


— 


FEMESH 


I 1 . 




1 1 


| 


1-1 -1 1 


■*>■■■■—« 


S.G.MILI7S0P0UL0S 


1-04/04/79 ! ™ 1 — 




i 1 


I 


ii>d<ii<ijo «••->•• 



J — r I 



'Omi«i WaUm*m1 



s=a 



MEjSH i G 



rrt 



.ld 



1 1 



FN£RAm 1 ON 



m 



1 1 



^2 
GO. 



eco 



1 1 



i '4 



i I i S 
TOT 



fTEST i ilPH INnTC 



I I 



Ml I 

200' 

"S CO" 



i mt nrn 



□TTI" 

PIT 



I I l 



MM 

Tilt 

J3QCJ. 

_6co; 



i i 



imii 



1 1 



nr 



MU 



310 



I i 



I ! I 



i i M LLMi 



I I 

ML 



I I I ! I I ill 



I I I 



I I 



I ! 



! I I 



i I II I 



! I 



! i I 



rm 



! ! 



TT 



Mill 



! ! ! I i 



i M ! i I I 



TTT 



i n ! 1 1 1 



I I 



1 1 



1 1 i 



i III 



I I 



ill 



I I 



I I 



I I 



I I i 



~rn 



MM 



I I I 

i — r 



l i 



TT 

TTI' 



jrrr 



TTT 



1 1 



! ; i 



i i ■ i 



i I 



TH" 



1TTT 



i I 



LlA 



Mil 



! I 



I i ! 



I I 



i I 



I I I I 



-T 



"H-r 



IMT 



1 : TT 
TT~|_i 

lift 



i ! I 



im 



TT 






! r; 1 1 

Mil! 

! : i m 



! ! i ! 

mi 



30 



. Q 




100. 50. 0. 



C_) = Node Number 
/ \ = Element Number 



Hll\ 72 NODES 
*£«/ 30 ELEMENTS 



The uncircled numbers indicate the dimensions of the 
mesh in inches. 

Figure 3.1 Example of Mesh. Generation 



31 



"he output of the example proolam using FHflESfl is as follows 



Output of Example Problem Using FEMESH 



3—3 M £ S H GENERATION T £ S T ( ? S I N T £ Q N L Y 



NOP 



LT G NC0E5 ONLY 



Fjfii'U 



-1 G£ Q SiP<+ 
L T Q a ^ S Y S 



NUMSES CF NOOES 1Z 



MY 
NZ 



« A T iLSJAL v -' u H c - £ 3 Q " <- - y £ 5 S ( go I T.C m t o to ?) 

1112 3 
,..C £0 >,g 



.aaa 



i a a . a a a 



.ggo 

■Z-. CO a a □ 



1CG.GCG 2GG.GGQ 5GG.QGG 31G.GGC 32G.CQG 



.GGG 2CG.GGG 4CG.GGG 6GC.GCG 



32 



Output of Example Problem Using FEMESH 



NOOE generation results 



1 




nnnp 


.nnnn 


p n n p 


2 




.CGGO 


I G U . G C G G 


.QGGC 


3 




n n n n 


7 p p . r, n n n 


. c a, n n 


4 




► GGGG 


iGG. GGGG 


.GGGG 


* 




.nnn p 


7 i p . n r. n n 


. -nnn 


6 




,ccaa 


32G.aCGG 


.GGGG 


7 


- r 


. r p r, n 


. q p p n 


. p P p p 


5 


5G 


.GGGG 


1GC.GGGG 


• GGGG 


Q 


5 G 


. n G G 


2PC.QGG0 


• GGGG 


1G 


SC 


.GGQG 


3 Q G . G C C G 


.GGOG 


i i 


5 G 


. n n n n 


71 n. anna 


.nnnn 


12 


5C 


.GGGG 


32G.GGGG 


.GGQG 


i ? 


i nn 


.rrqn 


. nc^ n 


,nn^n 


14 


1GG 


.GOOG 


iac .acac 


.coaa 


1 5 


i no 


.nnnn 


? p p .nnnn 


.nnnn 


16 


ica 


►GGGG' 


3GG.G0G0 


.GGGG 


1 7 


i nn 


. nrinn 


"in.nnnn 


. n a a a 


IS 


iaa 


.GGGG 


32G.GGGQ 


.GGGG 


1 o 




. rinnn 


.nrnr 


? n p . p. p p n 


2G 




.GGOG 


1CG.GCCG 


2GG.GGGG 


2 1 




. GGGG 


2 G G . a C G G • 


2GG .GGGG 


22 




,GOGC 


3GC.GC00 


2GC.GGGG 


77 




.nana 


7 1 g . a g a g 


2 a a . g a g a 


24 




.GGGG 


32G.GQCG 


2aa.GGGC 


75 


5 f! 


. n n n n 


.nnnn 


?r^.nn P P 


26 


50 


.gogg 


IGG .GGGG 


2QG.GGQC-. 


27 


sa 


.GGGG 


2GG.GCGG 


ZSCQCGG 


23 


5C 


.GCGG 


3CG .GGGG 


2QG.GGaa 


29 


5G 


.nncG 


3 1G.GGGG 


2 G a . G G U C 


3Q 


5G 


.GaaG 


32G.CGQG 


2aa.aaGG 


31 


iaa 


.GGGG 


.GGGG 


2GG.GGGC 


32 


iGG 


.GOGG 


IGG. GGQG 


2 G a . C G G ; 


33 


1GC 


.GQGC 


2GG..QCGG 


2 a G . G G G G " 



33 



Output of Example Problem Using FEMESH 



34 


1GG« 


GCOO 


3GG, 


.OGGO 


2 G G . o o a 


35 


LOG', 


a ooo 


3 1G 


, G 


2 c g . a a g c 


36 


IGG. 


gcog 


32G 


,GGCO 


200.0000 


37 




GOOG 




.caac 


i o a . c a a a 


33 




CGQO 


IGG 


.0000 


400 . GGGO 


39 




coaa 


2GG 


.GGOG 


4GC . GOOG 


40 




GCGG 


3GG 


.cccc 


4CC. GOOG 


U 1 




f .1 f* n 

Li u u U 


3 10 


.GGGC 


^00.0000 


42 




GGGO 


3 20 


.GGGC 


400. GCGG 


4 3 


f' Vt ' 


GGGC 




.OCCC 


40G..0aG0 


44 


50. 


aacc 


IGG 


,OOCC 


400.0000 


45 


5G . 


GOOG 


2CG 


.GCGG 


^OG .CCOC 


46 


5Q. 


.uOGC- 


3GC 


.GGOG 


4 00.0000 


47 


5G 


i ijGuu 


3 1G 


.GGGC 
.GGGC 


4 • . G 


43 


50. 


GCGG 


3 20 


4CG .CGGG 


uQ 


LOG 


GGCG 




. a o c c 


arc H o '1 n 


50 


IGG 


.GCGG 


IGG 


.GGCG 




51 


IGG 


.GGGC 


2CG 


.0000 

. GCGG 


u ; ' n n n n h 

"* '— >-j » U -j w Uj 


52 


IGG 


. C G u 


3GG 


ti n n " "■ n ~ 

" J tj • ^- ^ L-. w 


53 


IOC . 


caaa 


31G. 


GGOG 


400. GOOG 


Su 


1 HG . 


nnnn 


3?n 


nnnr, 


unn.nnnn « 


55 




GOOG 




.aoao 


60 0.0000 • 


Sft 




nnnn 


_ LOU 


.nnnn 


6 0.0000 . 


57 




GGGO 


200 


.0000 


60G.000C 


53 




ccoc 


3.C_C 


► ac.ac 


600.0000... 


59 




aoao 


310 


.OGGO 


6 a c . g a o a 


^n 




nnnn 


3 2.2- 


.nnnn 


600 . nnnn 


61 


50, 


,G000 




.oaaa 


60Q.G000 


A? 


sn 


nnnn 


\ n n 


.nnnn 


f*nn .nnnn 


63 


SO 


► aaca 


2CG 


.GOGO 


6 o c . a a o a 


^a 


50 


.nnnn 


vGG-.C 


600.0000 


65 


50 


,oaaa 


31G 


.aocc 


600 .GGGO 


r> 6 


sn 


.nnnn 


3 7 n 


.nnnn 


ann.nnnn 


67 


100. 


.caaa 




.GGOO 


6oa.aaoo 


^A 


1 nn 


.nnnn 


i nn 


.nnnn 


h n n , -n n n n 


69 


1GQ 


.oaoc 


200 


.gooc 


6oa.Gooa 


7n 


i nn 


.nnnn 


^nn. 


.nnnn 


^nn.nn n n i 


71 


100 


.oaaa 


310 


.0000 


6 g a . a o o o ; 


7? 


1 nn 


.nnnn 


.320. 


.nnnn 


r,nQ.nnn n ' 



34 



Output of Example Problem Using FEMESH 



ELEMENT GENERATION 3E.3U175 



I 


19 


25 


7 


2 


20 


26 


3 


1 


i 





? 


?<-< 


?i. 


a 


7 


7 ' 


7 ~ 


a 


i 


- 


n 





21 


27 


9 


4 


22 


25 


10 


1 


1 


a 


a 


77 


7a 


i P 


c 


7 ' 


?<3 


i i 


7 


1 


p 


5 


2 3 


29 


11 


6 


24 


30 


12 


3 


1 


a 


7 


7 c 


7 i 


1 7 


* 


7i. 


7? 


1 u 


i 


i 


p 


5 


26 


32 


14 


9 


27 


33 


1 5 


1 


i 





a 


77 


7 7 




i P 


7 3 


* 4 


i * 


1 


i 


p 


10 


23 


34 


16 


11 


29 


3 5 


17 


2 


1 


a 


1 i 


7 = 


7 C 


l 7 


i 7 


7 P 


"^ 


1 2 


7 


i 


n 


19 


37 


4 3 


25 


2D 


33 


44 


25 


1 


1 





?n 


7 3 


a u 


/ -» 


7 i 


7=s 


^ = , 


~ 7 


i 


i 


n 


21 


39 


45 


27 


22 


4 


4o 


2 5 


1 


1 


G 


7? 


tip 


UA 


-> 2 


7? 


4 1 


(I 7 


7a 


7 


i 


p 


23 


41 


47 


29 


2^ 


42 


43 


^ vj 


3 


1 


a 


?p 


a 7 


uo 


7 1 


76 


ua 


-n 


77 


1 


1 


p 


26 


44 


50 


32 


27 


4 5 


51 


.13 


1 


1 





^ 7 


u = 


=; i 


7 7 


75 


u ~ 


- ? 


" -!• 


1 


1 


p 


23 


46 


52 


34 


29 


47 


53 


3 5 


2 


1 


a 


7<3 


47 


S 7 


I = 


7P 


4 = 


S 4 

62 


44 


1 


1 
1 


(7 


37 


55 


6 1 


4 3 


33 


56 





7A 


So 


o7 


U 4 


7G 


=;7 


o T 


4 =; 


i 


1 


n 


39 


57 


63 


45 


tl o 
4 u 


53 


64 


46 


T 


1 


a 


UP 


t; 3 


~ 4 


u A 


U, 1 


c c 


o =; 


4 7 


7 


i 


p 


4 1 


59 


65 


47 


42 


60 


66 


43 


3 


1 





u ~ 


£ 1 


o7 


49 


4 a 


o 7 


-a 


= n 


i 


1 


p 


44 


62 


63 


50 


45 


63 


69 


51 


1 


1 





45 


63 


69 


5 1 


Uo 


6 4 


70 
71 


- 5 2 
53 


1 
2 


1 


a 


46 


64 


70 


52 


47 


65 


a 


47 


.. 6 .5 . 


7! 


S3 


u* 


66 


7 7 


=; u 


3 


1 


p 



35 



CHAPTER 4 
OPERATING INSTRUCTIONS FOR ANSYS 



4.1 WAVE FRONT SOLUTION AND LIMITATIONS 

The ANSYS program uses the wave front direct solution method for 
the system of simultaneous linear equations which are developed by 
the matrix displacement method. The frontal direct solution gives 
results of high accuracy in a minimum of computer time. 

There is no "band width" limitation in the problem definition . 
However, there is a "wave front" restriction . The "wave front"" " 
restriction depends on the amount of core storage available for a 
given problem . Up to 576 degrees of freedom on the wave front can 
be handled in a large core. An optional 1152 wave front is avail- 
able on very large computers. However, it is recommended not to 
exceed the 571 wave front if the CYBER 176 (CDC 7600) computer is 
used. The wave front limitation tends to be restrictive only for 
the analysis of three-dimensional structures or in the use of 
ANSYS in small computers. There is no limit on the number of 
elements used in a problem, but there is a limit on the number of 
elements which consist the wave front. The number of equations 
which are active after an element has been processed during the 
solution procedure is called the wave front of that point. 

For a banded solver, the band width is minimized by paying close 
attention to the ordering of the nodes. Alternatively, in the wave 
front procedure, the ordering of the element is crucial to minimize 
the size of the wave front. A degree of freedom becomes active when 
an element containing that degree is processed. 

That degree of freedom remains active in core until all elements 
containing that degree of freedom have been processed. Therefore, 
the element cards must be arranged in such a way, so that the element 
for which each nodal point is mentioned first is as close in sequence 
to the element for which it is mentioned last. 

The wave front must sweep through the model continuously from one 
end tcTThe other in the direction wmch has the largest number ot nodT 
points . The assembled matrix expands and contracts as nodal points 
make their first and last appearance in the element specifications. 
The optimum wave front for a simple line element model is a point; for 
a two-dimensional solid or plate element is a line of nodes; and 
for a three-dimensional solid, element is an area of nodes. 

An estimate of the wave front size can be made by multiplying the 
number of nodes in the wave front by the number of degrees of freedom 
per node. For example, consider the model shown in Fig. 3.1. The xz 
plane has the lesser number of nodes (3x4 = 12). Thus, the elements 
should be specified along the upper xz plane in the y direction. The 
new ordering of the elements is shown in Fig. 4.1. 



36 



If the elements described above have three degrees of freedom 
per node (say ux, uy, and uz), the maximum wave front size is approxi- 
mately 12x3 = 36. Often, it is convenient to generate elements with 
FEMESH in an order that is not the best for an optimum wave front. 
If so, elements may be internally reordered by ANSYS using the Fl cards. 

The Fl cards are called into the full ANSYS problem by inputting ' 
KORDER = 1 (column 78 of the C2 cards). A list of nodal points defining 
where the element reordering is to start is input on the first Fl card 
set. Additional lists may be defined to allow the user to guide the 
wave. The starting list usually consists of one node for a line element 
model , a line of nodes for an area element model, or a plane of nodes 
for a volume element model. There is a limit of 25 Fl cards or 1000 
nodes, whichever comes first. All elements attached to the first node 
in the list are defined first, then all elements attached to the second 
node are defined next, etc., until all elements attached to all nodes 
input on the first Fl card set (but not on later Fl card sets) are 
defined. 

This procedure is then repeated with the new set of nodal points 

brought in with the previously defined elements. If, during the course 

of reordering, an element would bring a node that is defined on a later 

Fl card set, that element is omitted until later. This feature allows 
the user to guide the wave front. 

The element reordering, using the Fl cards of the mesh shown in 
Fig. 4.1 from the mesh shown in Fig. 3.1 (generated by FEMESH), is 
presented in Table 4.2. It is recommended not to use the Fl cards if 
interface elements (connecting the slab to the subgrade) are used. It 
is rather easier to reorder the elements by hand. 

4.2 DATA INPUT INSTRUCTIONS 

Abbreviated ANSYS input instructions and the proper formats are 
included in this section. Specific quantities to be used for some of 
the variables are given in the Element Library (Chapter 5) for the 
various element types which to be used. Standard FORTRAN conventions 
are used for the input quantities. Variables with first letters from 
I to N are integers and must be riant justified (ending in the right- 
most column) in the specified field . No decimal point should be in- 
cluded. Variables with other first letters are floating point numbers 
and may be placed anywhere in the field. Floating point numbers should 
have the decimal point input. The exponent, if any, must be right 
justified in the specified field . 

No data should be punched on the cards in other than the specified 
fields. A blank input is treated as a zero or as a default option 
where indicated. Data cards must be in the order defined, and no add- 
itional cards (except for comment cards) are allowed. Comment cards 
may be inserted freely in the data deck. A comment card is identified 
by the characters C*** in columns 1 through 4. The remainder of the 
card is used for any comment that the user wants to have printed out 
along with the data input listing. All alphabetic labels (UX, FY, EX, 
END, etc.) must be left justified in their four space fields . Card 
sets requiring sentinel caras for termination are identified in the 

37 



tables. A card having only a -1 in columns 5 and 6 may be used for 
any sentinel card. All geometric input angles are in degrees and out- 
put rotations are in radians. Right hand coordinate systems are used 
throughout except where specifically noted . 

4.2.1 ANSYS Input Data for "Static Analysis (ANSYS/Rey. 2) 



CARD 



CI 



COLUMN(S) 
TITLE CARD 
1-30 



VARIABLE 



IHEDD 



MEANING 



ACCOUNTING CARD 



1-16 
18 



NAME 
NONOTE 



Title for output. If columns 77-79 are 
left blank and a comma punched in col- 
umn 80, the title may be continued on 
the following card. No limit. 



(Optional) User Identification Name. 

- Print notes (new features, modifi- 
cations, announcements, etc.) at 
end of solution. 



1 - Suppress printout of notes (con- 
tinued use not recommended). 
(Not Available) 

25-32 IACCNT (System Option) Account Number 

37-42 IEQRQD (Optional) Maximum number of equations 

in wave front (to check for adequate 
core storage) . 

75-30 ICORE (System Option) Core size parameter. 

Note - If no values are input, a blank card is still required. 

ANALYSIS OPTIONS 



1-4 

7 
11-12 



NSTEPS 

K20 

KTB 



16 



K15 



Number of load steps (one set of L 
through Q cards per load step) 
(-NSTEPS for an input data check run). 

- Static analysis 

- No element real constant table 

defined 

1 - Define up to 8 element real 

constants per table entry 
(Card D2). 

N - Define up to N (for N greater 
than 8) element real constants 
per table entry (Card D2). 

- No nodal force output. 

1 - Calculate and print out nodal 

forces for each element and tab- 
ulate reaction forces at specified 
displacement constraints. 



K2Q=0 



38 



CARD COLUMN(S) 

CI 
(cont.) 

16 



C2 



VARIABLE 



K15 



MEANING 



18 



K17 



- Print out reaction force tabula- 

tion only 

- Boundary conditions (.Cards N, 0, 

P, and Q) are linearly inter- 
polated within a load step. The 
full boundary conditions (as input) 
are used in the last iteration of 
the load step. 

- Boundary conditions are step 

changed at the first iteration 
to full values defined in the 
load step. 



22 



K23 



74-75 



KPROP 



N 



- No energy printout. 

- Calculate and print out elastic 
strain energy for each element. 

- Use polynomial material property 
equations. 

- Use linear interpolation in all 

material tables, up to N points 
per table (24 max.) . 

ANALYSIS OPTIONS (CONTINUED) 

1-12 TREF Reference temperature for thermal 

expansions. 

13-24 TUNIF Uniform temperature (used if no other 

temperatures are specified). 

ELEMENT TYPES - One card for each element type. End card set 
with an 1=0 card. 



2-3 


I 


Element type number 
between 1 and 20) . 


(arbitrary, 


5-6 


J 


Stiffness subroutine for this element. 
(A will cause this element type to 
be ignored). 


7 
8 
9 

10 
11 
12 


KEYSUB(IB) 

KEYSUB(IA) 

KEYSUBU) 

KEYSUBC2B) 

KEYSUBC2A) 

KEYSUB(2) 


Parameter KEYSUBU B) 
Parameter KEYSUBU A) 
Parameter KEYSUBU ) 
Parameter KEYSUB(2B) 
Parameter KEYSUB(2A) 
Parameter KEYSUB(2) 


for this subroutine 
for this subroutine 
for this subroutine 
for this subroutine 
for this subroutine 
for this subroutine 



14-15 



18 



KC If J-0, enter for KC the stiffness sub- 

routine number of the element type 
being ignored. 

INOTPR If 1, suppress all stress and force 

printout for this element type. 

(Return to next D card) 
K2Q=0 



39 



VARIABLE 



MEANING 



CARD COLUMN(S) 

D2 ELEMENT REAL CONSTANT TABLE - Clnclude this card set only if 

KTB is greater than Q on Card CI. The D2 cards may be repeated 
to form a table. End table with a blank (or 0.0 in the first 
field) card).. 

Element real constants (as given for 
element stiffness subroutine. Input 
constants in the same order as given. 

, Several cards may be required for 

71-80 RC(8) each table entry. Additional constants 

on cards are not used) . 



1-10, 


RCCD 


11-20, 


RC(2) 


21-30, 


RC(3) 



E 
El 



If a +00000 is punched in columns 1-6 and the rest of the card 
is left blank, suppress the element constant table printout. 
If -99999, cancel the suppression. 

If a +99999 is punched in columns 1-6 and a real number (D.) is 
input for RC(2) , this card represents D blank table entries. 

(Return to next D2 card) 

ELEMENT DEFINITION CARDS - one card set (El, E2) for each 

element - end with an I=-l card. 



ELEMENT DESCF.IPTION 
1-6 I 



7-12 



13-18,19-24, 
25-30,31-36, 
37-42,43-48 

49-54 



K, L, 
M, N, 

0, P 

MAT 



Number assigned to Node I on element 
(first node). If 99999, suppress 
element printout. If -99999, cancel 
the suppression. 

Number assigned to Node J on element 
(second node, if any) . 

Other node numbers, if required. 



Material number of this 
blank) . 



element (1 if 



55-60 



61-66 



ITYPE 



ITABLE 



Element type number for this element 
(1 if blank). (Refers to element 
types defined on D cards). 

- Element real constants, if any, are 
included on the next card (Card E2) 

K. - Element real constants are included 
at entry number K of the D2 card 
set. 



K2Q=0 



40 



CARD COLUMN (S) VARIABLE MEANING 

El 
(cont.) 

(The following three parameters are required only for 

■ or second level element generation). 

67-72 IiNUM If positive (first level generation), 

INUM is the total number of element 
sets generated (including the spe- 
cified set). The elements input on 
this and the next NEL-1 El. cards form 
the specified set. 

If negative (second level generation), 
-INUM is the total number of element 
groups generated (incl uding the NEL 
elements in the defined group). The 
defined group may include separately 
specified and/or first level generated 
elements. Columns 1-66 should be left 
blank. 

73-75 NINC Number by which to increment each 

element node number to generate suc- 
cessive element sets or groups. 
(Assumed 1 if left blank). 

76-78 NEL Number of elements in a specified set 

or a defined group to be repeated 
(assumed 1 if blank) . 

Element limit per set = 960/N (where 
N=8 or KTB, if KTB (Card CI) is 
greater than 8). No element limit 
per group. 

79-8Q KNEXT If positive, the tape unit for add- 

itional element input data (defaults 
to the current input file). 

If -1, all of the following elements 
have INUM added to each node number. 

E2 ELEMENT REAL CONSTANTS - (Include this card set only if the 

element has required real constants and if I i ABLE (on the 
preceding El card) is zero or blank). 

1-12, RC(1) Element real constants i^as given for 

13-24, RC(2) element stiffness subroutine. Input 

25-36, RC(3) constants in the same order as given. 

37-48, RC(4) Several cards may be required for each 

49-60, RC(5) table entry. Additional constants on 

61-72 RC(6) cards are not used). 

(Return to next El card) 
K20=0 

41 



CARD COLUMN(S) VARIABLE MEANING 

F NODE POINT LOCATIONS - One card for each node specified - 
and with an I--1 card. 

* 1-6 I If positive, I is the node number 

being defined (not a ]] numbers need 
to be used) . 

If zero (or blank), this card is used 
to define a local coordinate system. 

If negative, this card is used to 
define second level nodal point gen- 
eration. -I is the node number in- 
crement between successive nodal 
point groups. 

If 99999, suppress nodal point print- 
out. If -99999, cancel the suppression. 

7-3 KCS **"* If I is not zero **** 

- Nodes input (or generated in global 

cartesian coordinates. 

1 - Nodes input (or generated) in globa" 

cylindrical coordinates. 

2 - Nodes input (or generated) in global 

spherical coordinates. 
N - Nodes input (or generated) in local 
coordinate system N (N greater than 
2). 

***** If I is zero *"** 

- A local cartesian coordinate system 

is being defined. 

1 - A local cylindrical coordinate system 

is being defined. 

2 - A local spherical coordinate system 

is being defined. 

9-10 KFILL If I is positive **** 

- No first level nodal point genera- 
tion. 

N - Fill in nodes between the previously 
specified node and this one, incre- 
menting node numbers by N and 
linearly interpolating the coordinates 
(First level nodal point generation). 
(N must be positive) . 

K20=0 

42 



CARD 

F 
(cont. 



COLUMN(S) 
9-10 



VARIABLE 

KFILL 
(cont. ) 



MEANING 



*** If I ts zsro *** 

N - The local coordinate system being 
defined is identified as coordinate 
system number N (N greater than Z) . 



*■*■* 



N - 



If I is negative 



X'M jfc 



11-12 



!<NEXT 



The number of nodal points in the 
group to be repeated (defined on 
the following F cards). (Second 
level nodal point generation). 



*** If I is positive *** 

N - The tape unit number for additional 
nodal point input data (defaults to 
the current input file). 

*** If I is zero, KNEXT is not used *** 



*■*■* 



N - 



*-** 



If I is negative *** 

The total number of nodal point 
groups generated (including the 
defined group). (Second level 
nodal point generation). 

Special Combinations *"*"* 



If KNEXT=-1, all of the following node 
numbers have I (positive or negative) 
added to them. All other parameters 
on the card should be left blank. 

For defining nodal points use the appropriate node description 
column below. The THXY, .., THRP inputs are for nodal coordinate 
rotation. All angles are input in degrees. Use 3-0 input if a 
3-0 element is included in the D card set. 

For local coordinate system definition use Column 3 for origin 
translation and coordinate system rotation. 

For second level generation, inputs are incremental values. 
Increments and nodal- points must be specified in the same 
coordinate system (KCS). 



2-0imensional 
Rectangular Polar 



13-24 
25-36 
37-48 
49-60 
61-72 
73-80 



X 

Y 
THXY 



R 

THETA 
THRT 



(Return to next 
K20=0 



Cartesian 

X 

Y 
Z 

THXY 
THYZ 
THXZ 
F card) 



3-0imensional 

Cylindrical 

R 

THETA 

Z 

THRT 

THTZ 

THRZ 



Spherical 

R 

THETA 

PHI 

THRT 

THTP 

THRP 



CARD CQLUMN(S) VARIABLE MEANING 

H MATERIAL PROPERTY DEFINITIONS - the H card set CHI , H2) may 
be repeated. End with a LABEL=END card. 

HI -MATERIAL PROPERTY EQUATIONS 

1-4 LABEL LABEL identifying the property 

EX EY EZ ALPX ALPY ALPZ NUXY NUYZ 
NUXZ DENS MU GXY GYZ GXZ COPR NOPR 
END (Note - All labels are left justifies) 
(Only properties required by element 
material descriptions need be input. 
In addition, for isotropic materials, 
only the X (or XY) property label need 
be input) . 

5-8 MAT Material number (assumed 1, if left 

blank). 

12 KEY - Polynomial coefficients are input 

on this card. 

1 - A curve must be fit to the set of 

temperature vs. property data 
points listed on the following H2 
cards . 

2 - Fit curve as described for KEY=1 

and print out the fitting equation 
coefficients. 

3 - Use linear interpolation in all 

material property tables (input 
table on H2 cards). (Note, if KEY=3 
for any material, it must be 3 for 
all materials). 

13-24 CO Constant term in the property polynomial 

equation. 
Coefficient of linear term in equation. 
Coefficient of quadratic term. 
Coefficient of cubic term. 
Coefficient of quartic term. 

H2 MATERIAL PROPERTY TABLE - (Included only if KEY is greater than 

zero on previous HI card) 

First card - 

1-12 POINTS Number of temperature ys. property 

points in table. If KEY=1 or 2, at 
least 6 property points are required. 
If KEY=3, the number of points must 
not exceed the KPROP value input on 
Card CI. 



K20=0 
44 



25-36 


CI 


37-48 


C2 


49-60 


C3 


61-72 


C4 



CARD COLUMN(S) VARIABLE MEANING 

H2 
(cont. ) 

"I 3 " 24 TSTART Temperature corresponding to first 

property value input [required only 
if DELTAT is greater than zero). 

25-36 DELTAT Constant value by which, temperatures 

are incremented. Temperatures corre- 
spond to property values input on the 
next card(s) . 

Following cards - If DELTAT=0.0 (or blank), three temperature- 
property pairs may be input per card. Tem- 
peratures must be input in ascending order. 
If DELTAT is greater than zero, six properties 
may be input per card. Properties correspond 
to temperatures generated on first H2 card. 

(Continue table on as many cards as required, Format (6E12.2)) 
(Return to next HI card after table is complete). 

L-Q The following load cards (L-Q) are repeated NSTEPS (Card CI) 

times unless the repeating sets are terminated with a KDIS= <3 9 
card before the last expected (NSTEPS) set. 

L LOAD STEP DEFINITION 

1-3 KDIS 1 - Define new values for displacement, 

force, and pressure boundary condi- 
tions. Formulate new stiffness 
matrix. Zero all nonlinear terms 
and previous boundary conditions. 
- Use the previous displacement, force 
and pressure boundary conditions 
(do not include N, 0, or P card 
sets). Reformulate stiffness matrix. 
Continue nonlinear analysis. 
-1 - Change some of the previously defined 
displacement, force, and pressure 
boundary conditions (include changed 
values and N, 0, and P card set 
terminators). Also use unchanged 
previous bounc^ry conditions. Re- 
formulate stiffness matrix. Conti- 
nue nonlinear analysis. 
2 - Same as KDIS=1 except use previously 
formulated stiTfness matrix (speci- 
fied displacement constraints (on 
N cards) must be reseated (and all 
zero) ) . 

K20=Q 
45 



CARD COLUMN(S) 

L 1-3 
(cont. ) 



VARIABLE 



MEANING 



kdis -a 

(cont. ) 



4-6 



KTEMP 



99 - 

- 

1 - 

2 - 

3 - 
-N - 



Same as KDIS--1 , except use previ- 
ously formulated stiffness matrix 
Cspecified displacement constraints 
must remain zero) , 

Terminate the load card sets before 
the last expected set. An R or S 
card must follow. 

Set all temperatures to TUNIF 

(Card C2). 
Read in element temperatures on the 

Q cards for all elements. 
Read in nodal point temperatures on 

the Q cards. 
Use temperatures from previous load 

step. 
Use the temperatures calculated in 

the Nth cumulative iteration 

(file TAPE4) of a previous ANSYS 

heat transfer solution. 



7-9 



NITTER 



10-12 



NPRINT 



M 



The number of sub-step (or iterative) 
calculations to be done this load step 
(defaults to 1). Note, boundary con- 
ditions are linearly interpolated if 
,K17=0. If NITTER is negative, use 
covergence options (step boundary con- 
dition change imposed). 

Frequency of printout of stress, force, 
and displacement results - only every 
NPRINT iteration is printed out, begin- 
ning with iteration NPRINT. If zero 
or blank, suppress all printout for 
this load step . If negative, suppress 
boundary condition input printout only, 

For a negative value of NITTER, if 
NPRINT- NITTER , print the converged 
(or last) iteration. If NPRINT > 
NITTER , suppress all solution print- 
out. 



ADDITIONAL LOAD, PLOT, AND PRINT DEFINITION CARD 

The following four parameters may be used if more than three 
space fields are needed for the corresponding parameters on 
the L card. 



1-6 
7-12 



KDIS If non-zero, use instead of the value 

on Card L. 
KTEMP If non-zero, use instead of the value 

on Card L. 



K20=0 



46 



CARD COLUMN(S) VARIABLE MEANING 

M 
(cont.) 

13-18 NITTER If non-zero, use instead of the value 

on Card L. 
19-24 NPRINT If non-zero, use instead of the value • 

on Card L. 

N DISPLACEMENT DEFINITION CARDS - The N cards may be repeated. 

End with a LABEL=END card. 

1-6 I Node number at which displacement is 

specified. 

If 99999, suppress displacement printout. 
If -99999, cancel the suppression. 
If -2, add 12 to all the following nodes, 

7 IKEY If -j delete this displacement specifi- 

cati on . 

8-11 LABEL Direction of displacement. (In nodal 

coordinate system) 

UX UY UZ ROTX ROTY ROTZ PRES END 

13-24 DISP Value of displacement at this time 

(Radians for totations). 

37-42 12 If 12 is greater than I (for I positive), 

43-48 15 all nodes from I through 12 in stpes 

of 15 have this specified displacement 
(.15 is assumed to be 1 , if left blank) 

51-54, LABELS (5) Additional direction labels for which 

57-60,63-66, this displacement value applies at 

69-72,75-78 this node. 

(Return to next N card) 

Q FORCE DEFINITION CARDS - The cards may be repeated. End with 

a LABEL=END card. 

1-6 I Node at which force acts 

If 99999, suppress force printout 
If -99999, cancel the suppression 
If -2, add 12 to all the following nodes. 

8-11 LABEL Direction of force. (.In r\oda] coordinate 

system) FX FY FZ MX MY MZ 
FLOW END 

K20=0 



47 



CARD CQLUMN(S) VARIABLE MEANING 





(cont. ) 

13-24 FORCE Value of the force at this time. 

37-42 12 If 12 is greater than I (for I positive), 

all nodes from I thru 12 in steps of 
15 have this specified force (15 assumed 
to be 1 if left blank). 

(Return to next Q card) 

P PRESSURE DEFINITION CARDS - The P cards may be repeated. End 

with a blank (or 1=0) card. 

Pressures act in the element coordinate system. See Table 4.J.1 
for pressures available for element type J. 

1-6 I Element upon which pressure acts 

If 99999, suppress pressure printout. 
If -99999, cancel the suppression. 
If -2, add 12 to all the following 
elements. 

7-12 IFACE Face of element on which pressure acts. 

(If a super-element, IFACE is the 
load vector number) . 

13-24 PRESS Value of the pressure at this time. 

(If a super-element, PRESS is the 
scale factor for load vector IFACE). 

37-42 12 If 12 is greater than I, all elements 

from I through 12 in stpes of 15 have 
this pressure on this face (15 is 
assumed 1 if left blank). 

(Return to next P card) 

q TEMPERATURE DEFINITION CARDS - (Include this card set only if 

KTEMP-1 or 2 on Card L). 

Element temperature format (used if KTEMP is 1). One specifica- 
tion is required for each element, in the same order that the 
elements are specified. If KTEMP=2, use the node temperature 
format. 

1-8 Tl First temperature for this element. 



K2Q=0 



48 



CARD CQLUMN(S) VARIABLE MEANING 

Q ■ 9-16,... T2,.,. Second temperature, etc. 
(cont.) .;, 57-64 ...,T8 (Note - Fluences are also Input where 

applicable) , 

65-72 INUM If or 1, one element has this set of. 

temperatures. 

If N, the neat N elements (.counting 
this element) have these temperatures. 

73-74 KNEXT If positive, subsequent temperature 

input is to be from tape KNEXT (defaults 
to the current input file). 

76 KTCONT - All temperatures and fluences to 

be specified are contained on this 
card. 
1 - Additional temperatures and fluences 
continued on next card. 

Note - If KTC0NT=1 , T9 through T16 should be input on the next 
(second) card. The continuation card format is the same as the 
first card except that INUM and KNEXT are not used. Values not 
input are assumed to be zero. 

If a +99999 is punched in columns 1-6, suppress the element 
temperature printout. If -99999, cancel the suppression. 

(If all element temperatures have not 
been specified, return to next Q card). 

Nodal point -temperature format (used if KTEMP is 2). Nodal 
temperature specification cards may be repeated. Nodal 
temperatures not specified are set equal to TUNIF (Card C2). 
End nodal temperature set with an I=-l card. 

1-6 I Node number at which temperature is 

specified (if -1, end of nodal tem- 
perature input) . 

If 99999, suppress nodal temperature 
printout. 

If -99999, cancel the suppression. 

If -2, add 12 to all the following nodes. 

Specified nodal temperature. 

Specified nodal fluence. 

If 12 is greater than I (for I positive), 
all nodes from I through 12, in steps of 
15, have this temperature (15 is assumed 
to be 1 if left blank). 

K2Q=0 
49 



13-24 


TEMP 


25-36 


FLUEjNCE 


37-42 
43-48 


12 

15 



CARD CQLUMN(S) VARIABLE MEANING 

Q 

( cont -) (Return to next Q card) 

(Return to neat L card tf another load step is to be defined). 

S END OF DATA DECK CARD 

1-6 FINISH The word FINISH is punched in Columns 1-6 

of the last card of a problem data deck. 
Another problem data deck (oeginning 
with Card A) may follow. 



K20=Q 
50 



Oftentimes for real life problems, the engineer will have to use 
the 3rd Revision of ANSYS (Extended Core Version). To go from the 
2nd Revision to the 3rd one, set NSTEPS - Q [solution problem} or 
NSTEPS 3 -1 (model check problem) on card CI and finish with L-Q card 
sets with a KDIS-END card. 

4.2.2 ANSYS Input Data, for w«t Transfer Analysis (ANSYS/ Rev. 2) 

CARD COLUMN (S) VARIABLE MEANING 

A 

B 



TITLE CARD - See section 4.2.1 for data input instructions. 
ACCOUNTING CARD - See section 4.2.1 for data input instructions. 



CI ANALYSIS OPTIONS 

1-4 NSTEPS 



6-7 


K20 




1-12 


KTB 



1 
N 


16 


K15 



1 

2 


18 


K17 






32 



KAY(2) 



Number of load steps (one set of L 
through Q cards per load step). 
(-NSTEPS for an input data check run). 

-1 - Heat Transfer analysis. 

No element real constant table 
defined. 

Define up to 8 element real con- 
stants per table entry (Card 02). 

Define up to N (for N greater than 
8) element real constants per 
table entry (Card D2). 

No nodal heat flow rate printout. 

Calculate and print out nodal heat 
flow rate for each element and 
tabulate heat flow rates at speci- 
fied temperature constraints. 

Print out heat flow rate tabulation 
only. 

Boundary conditions (Cards N, 0, P, 
and Q) are linearly interpolated 
within a load step. The full bound- 
ary conditions (as input) are used 
in the last iteration of the load 
step. 
1 - Boundary conditions are step changed 
at the first iteration- to the full 
values defined in the load step. 

- First order integration for trans- 
ient solutions. 



<20=-l 

51 



CARD 

CI 
(cont. ) 



COLUMN(S) 
32 



74-75 



VARIABLE 

KAY(2) 
(cont. ) 



KPROP 



MEANING 



77 



K18 



1 - Second order integration for trans- 
ient solutions (recommended) 
(required for convergence or 
optimization procedures). 

- Use polynomial material property 

equations. 
N - Use linear interpolation in all 

material tables, up to N point 

per table (24 max. ) . 

- Nodal coordinate directions rotated 
for nodes input in global cylin- 
drical and global spherical coordi- 
nates (nodal x-axis is along input 
radius unless otherwise specified 
on F card. 



C2 



ANALYSIS OPTIONS (CONTINUED) 



13-24 



49-54 


NUMEL 


55-60 


MAXNP 


61-64 


KRSTRT 


65-68 


TOFFST 



69-75 



TUNIF Used only if KDIS=1 . If so, all nodal 

temperatures , the temperature boundary 
conditions (Card N) and the bulk tem- 
peratures (Card P) at the beginning 
of the load step are set to TUNIF. 
Also temperature dependent material 
properties are evaluated at TUNIF for 
the first iteration. 



Number of elements (required only for 
restart). 

iMaximum node number (required only for 
restart). 

The last load step already done, 
(restart key) . 

Degrees between absolute and of 
temperature system used (required for 
radiation) . 



TRSTRT Time at end of run to be continued 

(required only for restart}. 



ELEMENT TYPES - See Section 4.2.1 for data input instructions 

Note, the INOTPR parameter is used to suppress all heat 
flow printout for this element type. 



K2Q=-1 



52 



CARD COLUMN(S) VARIABLE MEANING 

D2 ELEMENT REAL CONSTANT TABLE - (Include this card set only if KTB 

is greater than on Card CI . 
See section 4.2.1 for data input 
instructions) . 

E ELEMENT DEFINITION CARDS - See Section 4.2.1 for data input 

instructions. 

F NODE POINT LOCATIONS - See Section 4.2.1" for data input instructions 



H .MATERIAL PROPERTY DEFINITIONS - See Section 4.2.1 for data input 

instructions. 

Note, the list of structural property labels (Cols. 1-4) should 
be replaced with the following thermal property identification 
list. 

KXX KYY KZZ DENS C HF OHMS VISC EMIS NOPR GOPR END 

L-Q The following load cards (L-Q) are repeated NSTEPS (Card CI) 

times unless the repeating sets are terminated with a KDIS=99 
card before the last expected (NSTEPS) set. 

L LOAD STEP DEFINITION 

1-3 KDIS 1 - Define new values for temperature, 

heat flow, and convection boundary 
conditions. Formulate new conduc- 
tivity and specific heat matrices. 
Zero all transient terms and pre- 
vious boundary conditions. 
- Use the previous temperature, heat 
flow, and convection boundary con- 
ditions (do not include N, 0, or 
P card sets). Re- formulate matrices 
Continue transient analysis. 
-1 - Change some of the previously de- 
fined temperature, heat flow, and 
convection boundary conditions 
(include changed value's and N, 0, 
and P card set terminators). Also 
use unchanged previous boundary 
conditions. Re-formulate matrices. 
Continue transient analysis. 



K20=-l 
53 



CARD COLUMN(S) 

L 1-3 
(cont.) 

4-6 



VARIABLE 

KDIS 
(cont. ) 



KTEMP 



MEANING 



99 - 

- 

1 - 

3 - 



Terminate the load card 
the last expected set. 
card must follow. 



sets before 
An R or S 



Set all internal heat generation 
rates to 0.0. 

Read in element internal heat gener- 
ation rates on the Q cards for all 
elements. 

Use heat generation rates from pre- 
vious load step. 



7-9 



NITTER 



10-12 



NPRINT 



M 



The number of sub-step (or iterative) ■ 
calculations to be done this load step 
(defaults to 1 ) . Note, if K17=0, 
boundary conditions are linearly inter- 
polated. If NITTER is negative, use 
steady-state convergence (step boundary 
condition change required) or transient 
optimization procedure. 

Frequency of printout of heat flows and 
temperature results - only every NPRINT 
iteration is printed out, beginning 
with iteration NPRINT. If zero or 
blank, suppress all printout for this 
load step ! If negative, suppress boun- 
dary condition input printout only. 

For a negative value of NITTER, if 
NPRINT= NITTER , print the converged 
(or last) iteration. If NPRINT > 
NITTER , suppress all solution printout. 

Time characterizing the end of this load 
step (If TIME is 0.0, blank, or less 
than the time of the previous load step, 
a steady-state solution is done). 

ADDITIONAL LOAD, PLOT, AND PRINT DEFINITION CARD 

The following four parameters may be used if more than three 
space fields are needed for the corresponding parameters on 
the L card. 

If non-zero, use instead of ' the value on 

Card L. 
If non-zero, use instead of the value on 

Card L. 
If non-zero, use instead of the value on 

Card L. 
If non-zero, use instead of the value on 

Card L. 

K2Q=-1 



13-24 



TIME 



1-6 


KDIS 


7-12 


KTEMP 


13-18 


NITTER 


19-24 


NPRINT 



54 



CARD COLUMN(S) 



VARIABLE 



MEANING 



N 



TEMPERATURE DEFINITION CARDS - The N cards may be repeated. End 

with a LABEL-END card. 



1-5 



I 



7 

3-11 

13-24 

37-42 
43-48 



IKEY 
LABEL 

TEMPER 

12 
15 



Node number at which temperature is 
specified. 

If 99999, suppress temperature printout. 
If -99999, cancel the suppression. 
If -2, add 12 to all the following nodes. 

If -, delete this temperature specifica- 
ti on . 

Input one of the following words 
(left justified) . 

TEMP PRES VOLT END 

Value of temperature (etc.) at this time. 

If 12 is greater than I (for I positive), 
all nodes from I through 12 in steps of 
15 have this specified temperature (15 
is assumed to be 1 , if left blank). 



(Return to next N card) 

CONVECTION DEFINITION CARDS - The P cards may be repeated. End 

with a blank (or 1=0) card. 



1-6 



I 



7-12 



13-24 



IFACE 



HCOEF 



25-36 



TBULK 



Element upon which convection acts. 
If 99999, suppress convection printout. 
If -99999, cancel the suppression. 
If -2, add 12 to all the following 
elements. 

Face-^f element on which convection acts. 
If a. super-element, IFACE is the load 
vector number. 

Value of the film coefficient at this 
time. Note, if KDIS-1 , the film 
coefficient at the beginning of this 
load step is also set to this value. 

If -N., use HF vs. TFILM equation input 
for material N on the H cards. 

If a super-element, HCOEF is the scale 
factor for load vector IFACE. 

Bulk temperature of adjacent fluid at 
this time. 



K2Q=-1 



55 



CARD COLUMN(S) VARIABLE MEANING 

P TBULK 

(cont. ) (cont.) 

37-42 12 If 12 is greater than I (for I positive), 
"43-43 15 all elements from I through 12 in steps 

of 15 have this convection on this face 
(15 is assumed to be 1 if left blank). 

(Return to next P card) 

Q HEAT GENERATION RATE DEFINITION CARDS - (Include this card set 

only if KTEMP-1 on Card L. One speci-' 
fi cation is required for each element, 
in the same order that the elements 
are specified) . 

1-3 HTGEN Internal heat generation rate for 
or CI this element. 

9-16, C2,— Constants defining polynomial equation 
— ,57-64 — ,C8 for variable heat generation rate 

(applicable to STIF71 elements). 

65-72 INUM If or 1 , one element has this rate. 

If N, the next N elements (counting 
this element) have this rate. 

73-74 i KNEXT If positive, subsequent heat generation 

rate input is to be from tape KNEXT 
(defaults to. the current input file). 

If a +99999 is punched in Columns 1-6, suppress the internal 
heat generation rate printout. If -99999, cancel the sup- 
pression. 

(If all element heat generation rates have not been specified 
return to the next Q card). 

(Return to next L card if another 
load step is to be defined) 

S END OF DATA. DECK CARD 

1-6 FINISH The word FINISH is punched in Columns 

1-6 of the last card of a problem data 
deck. Another problem data deck (begin- 
ning with Card A) may follow. 



•K20=-l 
56 



4.2.3 ANSY5 Input Data for Thermal Stress Analysis 

The thermal stress is equivalent to the static analysis except 
as follows: 

1. Save file TAPE 4 from heat transfer analysis. 

2. Assign file TAPE 4 to thermal stress analysis. 

3. Set KTEMP=-N (read temperatures fo the Nth iteration of 
previous heat transfer solution from file TAPE 4). 



Table 4.1 Element Reordering Instructions 

FIELD COLUMNS VARIABLE MEANING 

CARD Fl **** ELEMENT REORDERING INSTUCTIONS— Use as many cards as necessary 

to define a starting wave set. Use additional cards to define 

additional starting wave sets. End Fl card set with and Nl= 
END card. 

First node, second node, third 
node, etc., on starting wave. 
Continue on additional cards 
if necessary (Format 1216). 
12 67-72 N12 Blank fields are ignored. 

End starting wave list with 
a -1 node number. 



1 


1-6 


Nl 


2 


7-12 


N2 


3 


13-18 


N3 



(Return to next Fl card) 



57 



a 



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1 




1 : 


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<~\ 


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! 


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=r~ 


1 


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=i- 


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i 


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sj 


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i i 


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1 


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= 1 


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; 1 


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1 : 


! i 1 


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i s ! 


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i 1 


l i 1 


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i-i 


=1 | . : • 


i i 




! 


i 


I s ! 




[ l 


! i 


i i 




!ai ! 


=j 


r 


I 






■z\=. 


*j f ; 


ii ! 


1 


i ; 




; |*|i 


St 1 ' 


f ! 1 


! I 


: i 




|S|? 


si I 


y 


' i ' l 


j_ i 


i 


i |H| 


1 j ; 










! 








l=|j 


=i- 


i 








l s U 




! 




; i 


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\-U 


=t ■! 


1 


j | 




i . r is 




i 


! i 




|=|t 


i 










,1 I , 


1 : 


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— 


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.1 1 


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- i 1. i . 


I : 




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1 








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r»c5t-icj!cvji^-c3v — 


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, pjaSto^ssij 


I 






— -- 


i-iJ 


: i 


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58 



Y 




Sk 


A 


A 


A 


A 


A 



/\ = Element Number 



NX=3 

NY-6 
NZ=4 



ny)nz)nx 

NOTE THAT ThFoRDERING OF THE NOOES IS THE SAME AS IN FIGURE 3.1 
WAVE FRONT=(NX)(NZ) (DEGREES OF FREEDOM PER NOOE) 



Figure 4.1 Example of Element Reordering to Minimize 
the Wave Front 



59 



CHAPTER 5 
ELEMENT LIBRARY OF ANSYS 



5.1 ELEMENT SELECTION 

Table 5.1 is a summary of the available elements in ANSYS program. 
The above table lists the element identification number, the name, the 
number of dimensions, the number of degrees of freedom per node, the 
number of nodes, and some features. 

ANSYS models are either two-dimensional or three-dimensional, 
depending upon the element types used. Two-dimensional models must be 
defined in the x-y plane and the nodes must be input using the two- 
dimensional format on the F cards. Three-dimensional models must be 
defined in the x-y-z plane and the nodes must be input using the three- 
dimensional formate on the F cards. The element input is included on 
the ANSYS program data input cards as shown in Table 5.2. 

The degrees of freedom associated with the model should be suffi- 
cient to characterize the actual response. Including unnecessary degrees 
of freedom or selecting elements with unnecessary features increases 
the solution core size and running time. 

The units of the element input and output parameters are described 
in Table 5.3 in terms of force (F), length (L), time (t), temperature 
(T), and heat (Q). Mass units can also be expressed as Ft 2 /L. 

5.2 ELEMENT LIBRARY FOR STATIC ANALYSIS 

The three-dimensional isoparametric element (STIF45) and the 
three-dimensional interface element (STIF52) are recommended to use 
in a static analysis. 

5.2.1 Three-dimensional Isoparametric Solid Element 

The three-dimensional isoparametric solid element is a higher- 
order version of the three-dimensional elastic solid element (STIF5). 
The higher-order element gives a considerable improvement of accuracy 
over the constant strain element. The advantage of isoparametric 
elements over constant strain elements is that, for a given accuracy, 
the number of degrees of freedom necessary to describe the structure 
may be reduced. Accordingly, not only the data preparation time, but 
also the computer wave- front solution time is reduced. 

The element has plasticity, but no creep or swelling capabilities. 
If all capabilities are needed, STIF49 should be used. The isoparametric 
solid element is defined by eight nodal points having three degrees of 
freedom at each node: translations in the nodal x, y , and z direction. 

An option is available to print out the stresses and strains on 
particular element surfaces when the surfaces are fr^e surfaces of the 
structure. Other options are available to print stresses at the inte- 
gration points or at the nodes. A summary of the isoparametric solid 



60 



element parameters is given in Table 5.4. 

Input Data . The geometry, nodal point locations, face numbers, 
loading, and the coordinate system for this family of elements are 
shown in Fig. 5.1. The element is defined by eight nodal points and 
the material properties. The nodal points should be numbered in the 
order shown in Fig. 5.1. The number of nodes input on Card El defines 
the type of solid element used. The material" may. be orthotropic, with 
ten elastic constants required for its specification. The three addi- 
tional shear modulus terms are optional and may be included for a more 
complete description of the material. If not included, the values are 
computed from the other input properties. There are no real constants 
required for this element. 

The element loading can be either temperature gradients (specified 
by nodal temperatures) or pressures (on one or more faces), or a 
combination of both. 

The data input for the isoparametric solid element is as follows: 

1) only the eight node element with six pressure surfaces is available; 

2) plasticity capability is included; 3) printout is available on a 
second surface for elastic solutions, as the numerical integration 
points, and at the nodal points; 4) the incompatible displacement modes 
may be suppressed with KEYSUB(IB), and 5) the number of number integra- 
tion points may be selected for elastic solutions with KEYSUB(IA). 

Output Data . The solution printout associated with the isopara- 
metric solid element is summarized in Table 5.5. Figure 5.2 shows a 
schematic STIF45 element output. 

Theory . The element formulation includes incompatible displacement 
modes. Either a 3x3x3 or a 2x2x2 lattice of integration points is 
available for use with the numerical (Gaussian) integration procedure. 

Assumptions and Restrictions . Zero volume elements are not allowed. 
Elements may be numbered either as shown in Fig. 5.1 or may have the 
planes IJKL and MNOP interchanged. Also, the element may not be twisted 
such that the element has two separate volumes. This occurs most fre- 
quently when the elements are not numbered properly. The dihedral angle 
between adjacent element faces should be less than 180°. 

All elements must have eight nodes. A "triangular" shaped element 
may be formed by defining duplicate K and L and duplicate and P node 
numbers. The extra mode shapes are automatically deleted for 
"triangular" shaped elements so that a "constant strain" element re- 
sults. 

The first two lines of the element solution printout are valid for 
both isotropic and orthotropic materials. The principal strains (line 

3) are not valid for orthotropic materials. The principal stresses and 
the maximum shear stresses, however, are valid for orthotropic materials. 



61 



Surface stress outputs are valid only for isotropic elastic 
materials for which this face is a fr^e surface of the structure. 
Surface stresses should not be requested on the zero area face of 
"triangular" shaped elements. 

The 2x2x2 lattice of integration points is automatically used 
with plasticity solutions (K13 > on Card CI). 

5.2.2 Three-dimensional Interface Element 

The three-dimensional interface element represents two parallel 
surfaces in space which may maintain or break physical contact and 
may slide relative to each other. The element is capable of supporting 
only compression in the direction normal to the surfaces and shear 
(Coulomb friction) in the tangential directions. The element has 
three degrees of freedom at each node: translations in the nodal x, 
y, and z directions. 

The element may be initially pre-loaded in the normal direction 
or it may be given a gap specification. A specified stiffness acts in 
the normal and tangential directions when the gap is closed and not 
sliding. Because of the nonlinearity of the element an iterative 
solution procedure is required. A summary of the three-dimensional 
interface element parameters is given in Table 5.6. 

Input Data . The geometry, nodal point locations, and the coordi- 
nate system for the interface element are shown in Fig. 5.3. The 
element is defined by two nodal points, an interface stiffness, an 
initial gap (or interference, and an initial element status. The 
orientation of the interface plane (unlike STIF12) is defined by the 
nodal point locations. The plane is assumed to be perpendicular to 
the 1-0 line. The element coordinate system has its origin at node 
I and the x-axis is directed toward node J. The interface plane is 
parallel to the element y, z plane. 

The stiffness, k, may be computed from EA/L -- where the parameters 

are determined from the adjacent element. The effective length, L e «, 

is arbitrary, but may be on the order of 1/10 of the adjacent element 
length. The stiffness may also be computed from the maximum expected 
force divided by the maximum allowable surface displacement. In most 
cases k is several orders of magnitude greater than the other stiff- 
nesses in series with it so that its exact value is not critical. The 
initial gap (GAP) may be positive or negative. 'If negative, an ini- 
tial interference of this amount exists. The initial element status 
(START) is used to define the "previous" condition of the interface 
to be used at the start of the first iteration. This input overrides 
the condition implied by the gap specification and is useful in anti- 
cipating the final interface configuration and thereby reducing the 
number of iterations required for convergence. This parameter is also 
useful for inputting the element status in a run which is to be con- 
tinued, as determined from a previous ANSYS run. 



S2 



The only material property required is the interface coefficient 
of friction, u. A zero value should be used for friction less surfaces. 
Temperatures (used if u is temperature dependent) may be specified at 
the element nodes. For some problems, a loss of contact or a sliding 
at the interface isolates a portion of the structural model not having 
sufficient displacement constraints. The KEYSUB(l) option, therefore, 
may be used to maintain a small force across and along the interface, 
maintaining stability while causing only a negligible inaccuracy in the 
analysis. The KEYSUB(2) option may be used whenever friction may cause 
some gap elements to oscillate slightly between a sliding and a stick- 
ing status. 

Output Data . The solution printout associated with the three- 
dimensional interface element is summarized in Table 5.7. The value 
USEP is the normal displacement (in the element x-di recti on) betw een 
the interface surfaces at the end of this iteration, that is, USEP = 
(u ), - (u )- + GAP. This value is used in determining the normal 

force. Note, the normal force will not be an equilibrium value unless 
this iteration represents a converged solution. 

The value USLIDE is the accumulated amount of surface sliding at 
the end of this iteration. Sliding may occur in both the element y and 
z coordinate directions. Note, sliding occurs in the iteration after 
the limiting tangential force is exceeded. KTYPE describes the status 
of the element at the end of this iteration for use in the next itera- 
tion. The surface may be in rigid contact (KTYPE=1), sliding contact 
(KTYPE=2), or frze (KTYPE=3). If, for example, KTYPE* 3 at the end of 
an iteration, an element stiffness of zero is used for the next itera- 
tion. The KTYPE values may be input *or START if a new run is to 
continue from this iteration. 

If no other effects are present ':nd KEYSUB(2)=0, convergence 
occurs whenever the gap status remains unchanged. For a friction! ess 
surface, the converged gap status is either KTYPE=2 or 3. Whenever 
KEYSUB(2) > 0, an element having sliding force oscillations within a 
defined tolerance range on u F , resulting in an oscillating gap 

status (KTYPE=1 , 2, etc.), is accepted as converged. This tolerance 
range is usually within the uncertainty range of u. 

Theory . The displacement functions for the interface element 

can be separated into the normal and tangential directions since they 

are basically independent. In the normal (element x) direction, when 

the normal force (F ) is negative, the interface remains in contact 

n 

and responds as a linear spring. As the normal force becomes positive, 

contact is broken and no force is transmitted (unless !<EYSUB(1 )=1 , 

then a small force is supplied to prevent a portion of the structure 

from being isolated). 

In the tangential directions, for F < and the absolute value 
of the tangential force (F ) less than or equal to (u F n ), the inter- 
face does not slide and responds as a "linear spring in the tangential 



63 



direction. However, for F„ < Q and F„ > u F„ , sliding occurs. Note 

n s r n 

that F„ is a variable and if contact fs broken, the tanaential function 
n 

degenerates to a zero slope straight line through the origin (or of 
slope K/1Q\ if KEYSUB(IH) indicating that no Cor little) tangential 
force is required to produce sliding. Figure 5,4 shows the displace- 
ment functions for this element. 

Assumptions and Restrictions . The gap size may be specified 
independently of the nodal point locations. Nodes I and J, however, 
may not be coincident since the nodal locations define the interface 
plane orientation. The element is defined such that a positive normal 
displacement (in the element coordinate system) of node J relative to 
node I tends to open the gap. Recall that the element coordinate 
system is defined by the I and J node locations. The nodes defining 
the element may have arbitrarily rotated nodal coordinate systems 
since a displacement transformation into the element coordinate system 
is included. 

The friction coefficient may be input as a function of temperature 
and is evaluated at the average of the two node temperatures. For this 
nonlinear element an iterative solution procedure is required with the 
stiffness matrix re- formulation each iteration. Note, the effect of 
the element status changed in this iteration does not appear until the 
next iteration. Non-converged solutions are not in equilibrium. If 
GAP=0.Q (or blank), the element stiffness is included in the first 
iteration, unless START=3.0. 

The element operates only in the Static (K2O0) and the Nonlinear 
Transient Dynamic (K2Q=4) analyses. If used in other analysis types, 
the element maintains its initial status throughout the analysis. 
Note, a gap condition capability is also included in the Reduced Linear 
Transient Dynamic (K20=5) analysis. 

The element coordinate system orientation angles a and 8 (shown 
in Fig. 5.3) are computed by the program from the nodal point locations, 
a ranges from 0° to 360° and S from -90° to +90°. Elements lying 
along the +Z axis are assigned values of a=0°, S= + 90°, respectively. 
The element coordinate system for a=0°, 8=90° is shown in Fig. 5.3. 
Elements lying off the Z-axis have their coordinate system oriented as 
shown for the general a, 2 position. Note, for a=90°, 3^90°, the 
element coordinate system flips 90° at the Z-axis. 

5.3 ELEMENT LIBRARY FOR HEAT TRANSFER 

For a heat transfer analysis, it is recommended to use the iso- 
parametric quadrilateral temperature element (STIF55) and the two- 
dimensional conducting bar (STIF32). 

5.3.1 Isoparametric Quadrilateral Temperature Element 

The isoparametric quadrilateral temperature element can be used 
as a biaxial plane element or as an axisymmetric ring element with a 
two-dimensional thermal conduction capability. The element has four 



64 



nodal points with a single degree of freedom, temperature, at each node. 
The isoparametric temperature element. is a higher-order version of the 
two-dimensional linear temperature element (STIF35). The advantage of 
isoparametric temperature elements over linear temperature elements is 
that, for a given accuracy, the number of degrees of freedom necessary 
to describe the structure may be reduced. Accordingly, the data pre- 
paration time and the computer wave front solution time are also reduced. 

The isoparametric temperature element is applicable to a two- 
dimensional, steady-state or transient, Thermal (K20=-l) analysis. If 
the model containing the isoparametric temperature element is also to 
be analyzed structurally, the element should be replaced by an equiva- 
lent structural element. The nodal temperatures determined from the 
isoparametric temperature element are applied to the corresponding 
structural nodal points. A summary of the isoparametric quadrilateral 
temperature element parameters is given in Table 5.8. 

Input Data . The geometry, nodal point location, face numbers, 
loading and the coordinate system for the isoparametric temperature 
element are shown in Fig. 5.5 The isoparametric temperature element 
must have four nodes. 

The thermal conductivities are defined in the global X and Y 
directions. The specific heat and the density may be assigned any 
values for steady-state solutions. An average internal heat generation 
rate may be applied to the element. All of the element lateral surfaces 
have convection capability and are numbered as shown in Fig. 5.5. 

Output Data . The solution printout associated with the isopara- 
metric tamperature element is as shown in Table 5.9. 

Theory . The theory on which the isoparametric temperature element 
is based as described for the STIF35 element, except for the tempera- 
ture function. The temperature function in this element is not a 
linear polynomial, but includes additional incompatible temperature 
modes. 

A 3x3 lattice of integration points is used for the 
numerical (Gaussian) integration procedure. 

Assumptions and Restrictions . The isoparametric quadrilateral 
temperature element must not have a negative or a zero area. The 
element must lie in an X-Y plane and the X-axis must be the radial 
direction for axi symmetric problems. Also, axi symmetric structures 
should be modeled in the +X quadrants. 

A triangular elememt may be formed by defining duplicate K and L 
node numbers. The extra mode shapes are automatically deleted for tri- 
angular elements so that a linear temperature element results. Face 3 
should not be defined as a convection surface if nodes K and L are 
coincident. 

If the thermal element is to be replaced by an analogous structural 
element with surface stresses requested, the thermal element should be 
oriented such that face 1 and/or face 3 is a free surface. 



65 



5.3.2 Two-dimensional Conducting Bar 

The two-dimensional conducting bar is a uniaxial element with the 
ability to conduct heat between its nodal points. The element has a 
single degree of freedom, temperature, at each node point. The con- 
ducting bar is applicable to a two-dimensional (plane or axi symmetric) 
steady-state or transient Thermal (K20=-l ) analysis. 

If the model containing the conducting bar element is also to be 
analyzed structurally, the bar element should be replaced by an equiva- 
lent structural element. The node temperatures determined from the 
conducting bar element are applied to the corresponding structural 
element's nodal points. Structural elements accepting a transverse 
temperature gradient are given a uniform temperature in that direction 
by averaging the nodal temperatures. A summary of the two-dimensional 
conducting bar element parameters is given, in Table 5.10. 

Input Data . The geometry, nodal point locations, loading, and 
coordinate system for the conducting bar element are shown in Fig. 5.6. 
The element is defined by two nodal points, a cross-sectional area, and 
the material properties. Note that for an axi symmetric analysis, the 
area must be defined on a "per radian" basis. The specific heat and 
the density may be assigned any values for steady state solutions. The 
thermal conductivity is in the element longitudinal direction. An 
average internal heat generation rate may be applied to the element. 

Output Data . The solution printout associated with the conducting 
bar element consists of the node temperatures, T(I) and T(J), which are 
included in the overall nodal temperature solution printout. 

Theory . The temperature distribution for this element is obtained 
from the numerical- solution of the following equation: 

where K s thermal conductivity (Heat/Length*Time*Deg) 

p = density (Weight (or Mass)/Volume) 
C = specific heat (Heat/Weight (or Mass)*0eg) 

q ■ internal heat generation rate (Heat/Volume*Time) 
The temperature function is a, linear polynomial of the form: 

T(x) = C-J + C 2 x 

where the x-axis extends from node I to node J. 

Assumptions and Restrictions . Heat is assumed to flow only in the 
longitudinal element direction. The element must be in an X-Y plane 
and the global X-axis must be the radial direction for axi symmetric 
problems. The element must not have a zero length, so nodes I and J 
must not be coincident. 

66 



5.4 ELEMENT LIBRARY FOR THERMAL STRESS ANALYSIS 

It is recommended to use the two-dimensional isoparametric 
element (STIF42) and the two-dimensional interface element (STIF12) 
in a thermal stress analysis. 

5.4.1 Two-dimensional Isoparametric Element 

The two-dimensional isoparametric element is a higher-order version 
of the two-dimensional constant strain element (STIF2). The higher- 
order element gives a considerable improvement of accuracy over the 
constant strain element. The advantage of more complex elements over 
constant strain elements is that, for a given accuracy, the number of 
degrees of freedom necessary to describe the structure may be reduced. 
Accordingly, the data preparation time and the computer wave- front 
solution time is also reduced. The element has plasticity, but no 
creep or swelling capabilities. If all capabilities are needed, 
STIF2 should be used. 

The isoparametric element is defined by four nodal points having 
two degrees of freedom at each node: translations in the nodal x and 
y directions. The element may be used as a biaxial plane element or 
as an axisymmetric ring element. An option is available to print out 
the stresses and strains on particular surfaces of the element when 
the surfaces are free surfaces of the structure. .Other options are 
available to print stresses at the integration points or at the nodes. 
A summary of the two-dimensional isoparametric element parameters is 
given in Table 5.11 . 

Input Data . The geometry, nodal point locations, face numbers, 
loading, and the coordinate system for this element are shown in Fig. 
5.7. The element input data includes four nodal points, a thickness 
(for a plane stress option only) and the orthotropic material proper- 
ties. The element loading may be input as any combination of node 
temperatures, node fluences, and element pressures. The nodal forces 
should be input per unit of depth for a plane analysis (except for 
KEYSUBO ) s 3) and per radian for an axisymmetric analysis. 

The data input for the isoparametric element is as follows: 

1) only the four-node element with four pressure surfaces is available; 

2) creep and swelling capabilities are not included; 3) printout is 
avaiable on a second free surface for elastic solutions, at the numeri- 
cal integration points and at the nodal points; and 4) the incompatible 
displacement modes may be suppressed. 

Output Data . The solution printout associated with the two- 
dimensional isoparametric element is summarized in Table 5.12. Line 
K-L is analogous to line I -J except that it applies to the opposite 
surface. Figure 5.8 shows a schematic STIF42 element output. 

Theory . The element formulation includes incompatible displace- 
ment modes. A 3x3 lattice of integration points is used with the 
numerical (Gaussian) integration procedure. 



67 



Assumptions and Restrictions . The area of the element must be 
positive. Zero area elements will print out an error message and con- 
tribute nothing to the total stiffness. Negative area elements print 
out a warning message and will not plot correctly. The numbering of 
the nodes should be counter-clockwise in the coordinate system shown 
in Fig. 5.7. The two-dimensional isoparametric element must lie in 
an X-Y plane and the global X-axis must be the radial direction for 
axi symmetric problems. An axi symmetric structure should be modeled 
in the +X quadrants, 

A triangular element may be formed by defining duplicate K and L 
node numbers. The extra mode shapes are automatically deleted for 
triangular elements so that a constant strain element results. The 
surface stress printout is valid only for isotropic, elastic elements 
for which this face is a fr^e surface. Surface strains, however, are 
valid for both isotropic and orthotopic elements. Surface stress 
printout on an X=0 face of axi symmetric elements or on the zero length 
side of a triangular element should not be requested. 

5.4.2 Two-dimensional Interface Element 

The two-dimensional interface element represents two plane or 
axisymmetric surfaces which may maintain or break physical contact and 
may slide relative to each other. The element is capable of supporting 
only compression in the direction in the normal to the surfaces and 
shear (Coulomb friction) in the tangential direction. The element has 
two degrees of freedom at each node:, translations in the nodal x and 
y directions. 

The element may be initially pre-loaded in the normal direction or 
it may be given a gap specification. A uniform stiffness acts in the 
normal and tangential directions. Because of the overall nonlinearity 
of the element an iterative solution procedure is required. A summary 
of the two-dimensional interface element parameters is given in Table 
5.13. 

Input Data . The geometry, nodal point locations, and the coordi- 
nate system for the interface element are shown in Fig. 5.9. The 
element is defined by two nodal points, an angle to define the inter- 
face plane, a stiffness, an initial displacement interference, and an 
initial element status. The stiffness, if left eq ual to zero, defaults 
to 10 s . An element coordinate system (x-y) is defined on the inter- 
face plane. The angle 9 is input in degrees and is measured from the 
global X axis to the element-x axis. Note, the orientation of the 
interface plane is defined by. the angle 9 and not by the nodal point 
locations. 

The stiffness, k, may be estimated from EA/L -- where the para- 
meters are determined from the adjacent element. The effective length, 
L-xra is arbitrary, but may be on the order of 1/10 of the adjacent 

element length. The stiffness may also be computed from the maximum 
expected force divided by the maximum allowable surface displacement. 
In most cases k is several orders of magnitude greater than the other 



68 



stiffnesses in series with it so that its exact value is not critical. 
The stiffness should be "per radian" for an axt symmetric analysis. 

The initial displacement interference, 6, defines the displacement 
interference (if positive) or the gap size (.if negative). The Initial 
element status (START) is used to define the "previous" condition of 
the interface to be used at the start of the first iteration. This 
input is used to override the condition implied by the interference 
specification and is useful in anticipating the final interface confi- 
guration and reducing the number of iterations required for convergence. 
This procedure may also be used to continue a previous analysis . 

The on.ly material property required is the interface coefficient of 
friction, u. A zero, value should be used for friction less surfaces. 
Temperatures may be specified at the element nodes. For some problems, 
a loss of contact or a sliding at the interface isolates a portion of 
the structural model not having sufficient displacement constraints. 
The KEYSUB(l) option may be used to maintain a small force across and 
along the interface, maintaining stability while causing a negligible 
inaccuracy in the analysis. The K£YSUB(2)=1 option should be used 
whenever friction is present and there is the possibility of some gap 
elements oscillating slightly between a sliding-sticking status. 

Output Data . The solution, printout associated with the two- 
dimensional interface element is summarized in Table 5.14. 

The value USEP is the normal displacement between the interface 
surfaces at the end of this iteration, that is: USEP = (u ) , - (u w ) T - <3 

y « y i 

This value is used in determining the normal force. For an axi symmetric 
analysis, the element forces are expressed per radian of circumference. 
The value USLIDE is the accumulated amount of surface sliding at the end 
of this iteration. 

KTYPE describes the status of the element at the end of this itera- 
tion. It KTYPE=1 , the gap is closed and no sliding occurs. If KTYPE=3, 
the gap is open. If at the end of an iteration KTYPE=3, an element 
stiffness of zero is used for the next iteration. A value of KTYPE=+2 
indicates that node J moves to the right of node I as shown in Fig. 5.9. 
KTYPE=-2 indicates a negative slide. If no other effects are present 
and KEYSUB(2)=0, convergence occurs whenever the element status remains 
unchanged. For a frictionless surface (u=0.0), the converged element 
status is either KTYPE=+2 or 3. Wherever KEYSUB(2) > 0, an element 
having sliding force oscillations within a defined tolerance on 
U F , resulting in an oscillating element status (KTYPE=1, 2, etc.), 

is accepted as converged. This tolerance range is usually within the 
uncertainty range of u. 

Theory . The displacement functions for the interface element can 
be separated into the normal and tangential directions because they are 
basically independent. 

In the normal direction, when the normal force (F ) is negative, 
the interface remains in contact and responds as a linear spring. As 



59 



the normal force becomes positive, contact is broken and no force is 
transmitted (unless KEYSUB(1 )*1 , then a small force is supplied to 
prevent a portion of the structure from being isolated). 

In the tangential direction, for F < Q and the absolute value of 

the tangential force (F ) less than or equal to (u F ), the interface 

x y 

does not slide and responds as a linear spring in the tangential direc- 
tion. However, for F < and F > u F , sliding occurs . Note that 

y x y 

F v is a variable and if contact is broken, the tangential function 

A 

degenerates to a zero slope straight line through the origin (or of 
slope k/10 5 , if KEYSUBOH ) indicating that no (or little) tangential 
force is required to produce sliding. Figure 5.10 shows the displace- 
ment functions for this element. 

Assumptions and Restrictions . The gap interference is specified 
independent of the nodal point locations. Nodes I and J may be coin- 
cident since the orientation of the interface plane is defined only by 
the angle 8. The element is defined such that a positive normal dis- 
placement (in the element coordinate system) of node J relative to 
node I tends to open the gap, as shown in Fig. 5.9. If, for a given 
set of conditions, nodes I and J are interchanged, or if the interface 
is rotated 8 + 180°, the gap element appears to act as a hook element, 
i.e., the gap closes as the nodes separata. The element may have 
rotated nodal coordinates since a displacement transformation into the 
element coordinate system is included. 

The friction coefficient is evaluated at the average of the two 
node temperatures. The two-dimensional interface element must be de- 
fined in an X-Y plane and the global X axis must be the radial direc- 
tion for axi symmetric problems. The element operates only in the 
Static (K20=0) and the Nonlinear Transient Dynamic (K20=4) analyses. 
If used in other analysis types, the element maintains its initial 
status throughout the analysis. Note, a gap condition capability is 
also included in the Reduced Linear Transient Dynamic (K20=5) Analysis. 

No moment effects are included due to nodal points offset from a 
line perpendicular to the interface. If INTERFERENCE is zero (or 
blank), the element stiffness is included in the first iteration, un- 
less START = 3.0. The element requires an iterative solution with 
the stiffness matrix reformulated each iteration. Note that if the 
element status changes within an iteration, the effect of the changed 
status is included in the neat iteration non-converged iterations are 
not in equilibrium. 



70 



TABLE 5.1 
ELEMENT SUMMARY 7A3LE 



STIfFMgSS 
NO. 



NAHg 



6 

a 

9 

10 

1 1 
12 
13 

u 

13 

16 
17 

la 

19 
20 

21 
22 
23 
2* 
25 

26 
27 
23 
29 

30 

31 
32 
23 
34 
35 

36 

37 
33 
39 
^0 



3?AP, 2-0 

CONSTANT STRAIN .ELEH . 
EL-ST'C 3EAM-, 2-3 
ELASTIC 5EAM-. 3-3 
ELASTIC SOLID (C3T) 

SLAS- "LA7 TRI. PLATE 

S?AR» 3-0 

ELASTIC STRAIGHT PIPE 

CA3LE 



AXlSYM. CONICAL SMELL 

INTERFACE ElEM. (2-01 

EL if- FLAT TPT. SMELL 

S?RING-DAMP£R 

MASS WITH PqTaRY INER. 



MASS* 2-0 
MASS* 3-0 
SPRING* 2-0 

OAMPEP » 2-0 

PLASTIC STRAIGHT PIPE 

GENERAL M^ss 
COPE SPACED ANO GAP 
PLASTIC 3EAM-, 2-0 
TOPS ION 5PRING-0A.MPEP 
AXIS?*. HARMONIC QUAD. 

PLAS. FLAT 7RI. PLATE 
STIFF, DAMP, "A55 MATRIX 
PL FLAT SMELL (3 TEMP) 
CURVED PIPE (EL30VO 
CONDUCTING SOLID 

RADIATION LINK 
CONDUCTING 3AR, 2-0 
CONDUCTING pap, 3-0 
CONVECTION L INK 
LINEAR TEMPER. EL. 



NOUCTANCE 

>ci I 



HYO° iULlC 

CONQUC'I^G FLAT SH; 
FLUID COUPLING 
SLIDING INTERFACE 
COM3 InaT ION ELEVEN - 



OIH. 

2 

I 

2 
3 
3 

2 
3 
3 
3 

2 
2 

3 

2>3 

2 

2 

3 
2 

? 
3 

2>3 
2 
2 
3 
2 

2 
3 
3 
3 
3 



2 OH 
2 
3 

2 OR 
2 



OP 
3 
OR 
OP 
OR 



OOF NODES TYPE 



2 

3»A 

2 

2 

A-»6»3 

3 
2 
2 
2 

2 
2 
3 
2 

1 

1 
1 
2 
2 
2 

1 
2 
2 

2 

A 

3 
2 

3 

3 

At 6 »-3 

2 
2 
2 
2 
3*4 

2 
3 
2 
2 
2 



PLASTIC 

PLASTIC 

LINEAR 

LINEAR 

LINEAR 

LINEAR 
PLASTIC 
LINEAR 
NON-LIN 

LINEAR 
NON-LIN 

LINEAR 
LINEAR 
LINEAR 

LINEAR 
LINEAR 
LINEAR 
LINEAR 
PLASTIC 

LINEAR 

NON-LIN 

PLASTIC 

LINEAR 

LINEAR 

PLASTIC 

LINEAR 

PLASTIC 

LINEAR 

LINEAR 

NON-LIN 
LINEAR 

LINEAR 
LINEAR 
LINEAR 

NON-LIN 
LINEAR 
LINEAR 
NO N -LIN 
NON-LIN 



USE STIF21 



USE 
USE 

USE 
USE 



STIF21 
3TIF21 
5TIF1A 
STIFIA 



USE STIF14 



USE STIFiQ 



(CONTINUED ON NEXT PAGE) 



71 



"A8LE 



I (CONTINUED) 



ST IF r nESS 
MO- 



NAME 



OI». 



DOF 



NOOES TYPE 



4i 3—3 ELAS..CUAO. MEMS. 

42 LINEAR STRAIN I3QPAP. 

43 EL AS- FLAT PECT. SHELL 
4-A, TiPEPED UNSYM.. SEAM 

43 ISOPARAMETRIC SOLID 

46 ELAS. PLAT PECT. PLATE 

47 TSANSV.HT.CCNO. SHELL 2 

43 PL. PLAT SHELL !S TEH?) 

49 PLASTIC SOLID 

50 SU?EP-EL£H£NT 

32 INTERFACE ELS*. (3-0) 

53 LAMINATED 5HELL 

54,. TAPER. UNSYM. SEAM (2-0) 

53 ISCPAP.QUAO.TEHP.ELEM 

56 FLUID FL-HT TRANS PIPE 

57 ISO. QUAD. SHELL TEMP. 
53 PLASTIC HINGE ELEM. 

59 IMMERSED PIPE ELEM. 

60 PLASTIC EL50W 

61 A^IS7H. HARMONIC SHELL 

62 2-0 WAVE ELEMENT 

63 ELAS. "LaT CUaO. SHELL 

65 3-0 *AYE ELEMENT 

66 TPANS. THEPM-fLOW PIPE 

67 HT TPANS-ELECTPIC CUAO 
63 HT TPANS-ELECTPIC LINE 

69 HT TPAN-ELECTPIC SOLID 

70 ISO, CONOUCTING SOLID 

71 LUMPED 7HEPMA>_ MASS 2 
73 AXISY HARMONIC TEMP EL 



3 


3 


4 


LINEAR 


2 


2 


4 


PLASTIC 


3 


6 


4 


LINEAR 


3 


6 


3 


LINEAR 


3 


3 


3 


PLASTIC 


2 


3 


4 


LINEAR 


OP 2 


1 


5 


LINEAR 


3 


6 


3 


PLASTIC 


3 


3 


4.6.3 


PLASTIC 


3 


• 


- 


LINEAR 


3 


3 


2 


NON-LIN 


3 


6 


3 


LINEAR 


2 


3 


2 


LINEAR 


2 


I 


4 


LINEAR 


3 


2 


2 


NON-LIN 


3 


1 


4 


LINEAR 


3 


6 


2 


NON-LIN 


3 


6 


2 


LINEAR 


3 


6 


3 


PLASTIC 


2 


4 


2 


LINEAR 


2 


2 


4 


LINEAR 


3 


6 


4 


LINEAR 


3 


2 


3 


LINEAR 


3 


2 


2 


NON-LIN 


2 


2 


4 


ITERATIVE 


3 


2 


2 


ITERATIVE 


3 


2 


3 


ITERATIVE 


3 


1 


3 


LINEAR 


CP 3 


1 


1 


LINEAR 


2 


1 


4 


LINEAR 



72 



Table 5.2. Input of Element Parameters on 
ANSYS Program Data Cards 



Input 



Element- Parameter 


on Card 


NODS NUMBERS 


El 


REAL CONSTANTS 


02 or E2 


TEMPERATURES, FLUENCES 


Q. 


•PRESSURES 


P 


HEAT GENERATION RATES 


a 


CONVECTION SURFACES 


P 


MATERIAL PROPERTY EQUATIONS 


H 


KEYSU8(N) 






Table 5.3. Units of Input and Output Parameters 



Input Parameter Un i ts 

Area L 2 

Volume \? 

Pressure F/L 

Moment of Inertia L 

Fluence (?t) Neutrons/L 

Density M/l 3 

Convection Coefficient Q/L -t-T 

Conduct i vi ty Q/L-t-T 

Specific Heat Q/M-T 

Heat Generation Rate Q/l -t 

(except for STIF71 ) (Q/t) 

Spring Constant F/L 

Damping Coefficient F-t/L 

2 

Rotational Inertia F-^-t 



2 



Output Parameters Units 

Stress F/L 2 

Strain 

Moment or Torque L-F 

Twist Radians 

Heat Flow Rate Q/t 



74 



TA3LE 5.4. 
ISOPARAMETRIC SOLID ELEMENT - THREE IMENSIONAL 



SUSPOUTINE NAM£ 

NO. C. c NODES PER ELEMENT 

DEGREES Or FacZOQH ?€5? NOCE 

R£<3UTfi£0 RE-L CONSTANTS 

TEMPERATURES 

PRESSURES 

MATERIAL PROPERTY EOUATIONS 

MATRTCES CALCULATED 

PLASTICITY 

CREEP ANO SWELLING 

FORCES SAVED ON TAPE 

KEYSU3U) 

KEYSuS(lA) 



KEYSU3(13> 



STIFFS 

a 

3 

3 
6 



I»J»KtL»M,N»0»P 

UX.UYtUZ 



10 



TCI) »T(J) ,T<K) ,T(L) »T(H) ,7(N) » 

T(O) ,T(P) 
P(IJXL) jP (IJNM) ,P(JKON) ,?(KLPO) , 
P(LIMP) »P(NHCP) 

EX ♦ EY , EZ y ALPX » ALPY , Al_PZ > 
NUXY ,NUTZ >NUXZ » OENS . 
GXY*GYZ>GXZ (OPTIONAL) 



HASSt STIFFNESS 

YES 

NO 



- GENERAL 3-0 APPLICATION 

1 - GENERALIZED PLANE STRAIN OPTION 

- USE 3X3X3 LATTICE CF INTEGRATION POIN 

(USED FOR INCREASED ACCURACY WITH 
WARPED ELEMENTS ANO ELEMENTS HAVING 
HIGHLY NON-RECTANGULAR SHAPES) 

1 - USE 2X2X2 LATTICE OF INTEGRATION POIN 

(KEYSUS(IA) IS INTERNALLY SET TO 1 F 
PLASTICITY SOLUTIONS) 

- DISPLACEMENT FORMULATION INCLUDES Th.E 

EXTRA HOOE SHAPES 

1 - DISPLACEMENT FORMULATION OOES NOT 

INCLUDE THE EXTRA MODE 5HAPE5 



(CONTINUED ON NEXT PAGE) 



75 



TA8LE 5.4 (CONTINUED) 

XEYSU3(2) C - NO SURFACE STRESS OUTPUT 

1 - PRINT GUT STRESSES FOR SURFACE 2 

2 - PRINT GUT STRESSES FOR 5GTK SURFACES 

2 AiNO ; 

(SURFACE STRESSES AVAILABLE FOR 
ISOTROPIC, ELASTIC MATERIALS ONLY) 

3 - PRINT GUT SOLUTION AT EACH INTEGRATION 

POINT AS WELL AS AT CSNTROIO 
(FOR PLASTICI7C SOLUTIONS ONLY. 
NOTE - AOOS 21 MORE LIMES ? c 3 SLZ&EIT) 
3 - PRINT STRESSES AT THE 3 NODES AS WELL 

AS AT CSNTROID 

SUBROUTINE GATE V 30/72 

X V I T * XXXXXXXXX ** 9' M X M . T M ■ ? W W X ' J F X » ■ • M ^t f H^I A M A A A A * A A ■ ' X ' J J TT » W J f M. X X - ■ M 



76 



TABLE 3.5 
ISOPARAMETRIC SOLID ELEMENT - THREE OIMSNSIONAL 
EL£M£?*T PRINTOUT EXPLANATIONS 



EXPLANATION 



LAoEL 


NUMBS?. 
C3NSTA^ 


0? 
ITS 


FOP MAT 


LINE 1 








SQL in 
NOOSS 

xc»rc»2C 

TEMP 


1 

a 

3 

1 




15 

ais 

3F3.3 
F5.0 


LINE 2 








EPS 


6 




6F9.6 


SIG 


6 




6F3.<3 


LINE 3 








SIGPo 

TAUMaX 

EP?R 

VOL 

VM 


3 
i 

3 

1 
1 




3F3.0 

F7.0 

3F9.6 

F12.3 

F3.0 



ELEMENT NUMBER 

MOOES I>J->K,L»H,N,0»P 

X,Y,Z COORD I?JAT£3 OF ELEMENT CcNTROID 

ELEMENT AVERAGE TEMPERATURE 



E?X»E?Y,E?Z>GAMMAXY»GAMMAYZ»GAHMAX2 (GLOBAL 

(ELASTIC STRAIN COMPONENTS) 
SIGX»SIGY»5IGZ>TAUXY>7AUYZ>TAUXZ (GLOBAL J 



PRINCIPAL STRESSES SIG1 ,S IG2 >SIGD 

MAXIMUM S'ritM^ STRESS 

PRINCIPAL STRAINS ER1 , E?2 . E?3 (ISOTRCP-IC 

ELEMENT VOLUME 

VON MI3ES EOUIVALENT STRESS 

LINE IJNM SURFACE 2 STRESS CONDITIONS (PRINTED ONLY IF x£YSUS<2) IS 

GREATSp THAN ZERO) 

SURFACE AREA 

AVERAGE SURFACE TEMPERATURE 
SIGX» SIGYt AND TAUXY 
(X AXIS PARALLEL TO TM£ AVERAGE Or LINES 
I- J ANO M-N) 
VMS 1 F3.0 VON MISES EOUIVALENT STRESS FOR THIS FACE 

LINE IJNM SURFACE 2 STRESS CONDITIONS (CONTINUED) 

MAXIMUM* MINUMUM* ANO MAXIMUM SMEaR STRESS 
ON SURFACE 2 OF THIS ELEMENT 

ANGLE OF PRINCIPAL STRESSES (MEASURED FROM 
LOCAL X TOWAflO LOCAL Y) 

EPSX. E?SY, ANO GAMMAAY 

SURFACE PRESSURE 

(CONTINUED ON NEXT PAGE) 



AREA 


1 


F10.A 


TEMP 


1 


F<9.0 


XY STR 


3 


3F3.0 



HAX-MlN STR 


3 


3F3.0 


A 


1 


F5.1 


STRAINS 
PRESSURE 


3 

1 


3F9.Q 

~ Fa.o 



77 



TA6LE 5.5 (CONTINUED) 

LINES KL?0 SURFACE <* STRESS CONDITIONS (PRINTED ONLY IF" *SYSUS(2) = 2) 

(SAME AS SURFACE 2 OUTPUT 3UT APPLIED To SURFACE <*> 

LINES 4 ANO 5 NONH-INEAS SOLUTION (PRINTED ONLY IF K13 IS GREATER THAN 

ZERO ON CAPO CD 

SRPLAV 6 6F10.7 AVERAGE PLASTIC STRAINS AT CENTROIO 

(X*Y,Z»XY,YZ>*Z) 
SPORiV 6 6F10.7 AVERAGE ORIGIN SHIFT STRAINS AT CENTROIO' 

LINE 6 NON-LINEAR SOLUTION (CONTINUED) 

EPGNAV I FI0.7 AVERAGE GENERALIZED STRAIN AT CENTROIO 

ROSGAV 1 F1Q.4 AVERAGE GENERALIZED POISSONS RATIO 

AT CENTROIO 
SIGEiV 1 F10.2 AVERAGE EQUIVALENT STRESS AT CENTROIO 

NOTE - STRESSES ANO STRAINS ARE PRINTED A?TER THE PLASTICITY CORRECTIONS. 



78 



TABLE 5.3 
INTERFACE ELEMENT - T iREE-OIMENSlCNAL 

SUBROUTINE NAME STIF3E 

NO. Or NODES PER ELEMENT 2 I>o 

0EGPEE"S OF FREEDOM P*R NOOE 3 UX»UY»UZ 

REQUIRED SEAL CONSTANTS 3 STIFFNESS >GAP , START 

A NEGATIVE GAP ASSUMES A.N INITIAL 

INTERFERENCE CONDITION 
IF START = 0.0 OP BLANK, PREVIOUS STA 

OF ELEMENT DETERMINED FROM GAP INPUT 
IF STAPT = l.Ot GAP PREVIOUSLY CLOSED 
. AND NOT SLIDING 
IF STAPT =2.0* GAP PREVIOUSLY CLOSED 

AND SLIDING 
IF STAPT * 3.0* GAP PREVIOUSLY OPEN 

TEMPERATURES Z T(I)»T(J) 

PPESSijRES 

MATERIAL PROPERTY EQUATIONS 1 HU 

MATRICES CALCULATED STIFFNESS 

PLA-5TICITY NO 

NON-'-INE-R YES (ITERATIVE SoL'JTIcn REQUIRED) 

FORCES SAVED ON TAPE 2 NORMAL FORCE (FN )» TANGENTIAL FGPCE(FS) 

KEYSUB(l) - NO STIFFNESS ASSOCIATED WITH SEPARATED 

INTERFACE 
1 - STIFFNESS»1.0E-6 ASSOCIATED WITH 

SEPARATED INTERFACE FOR NORMAL MOTION 
ANO WITH SLIOING INTERFACE FOR 
TANGENTIAL MOTION 

XEYSUP<2) - CONVERGENCE BASED ON UNCHANGING GAP STATU 

1 - CONVERGENCE 3ASED ON CHANGING GAP STATUS 

WITHIN A 5 PERCENT UNCERTAINTY ON MU" 

2 - CONVERGENCE BASED ON CHANGING GAP STATUS 

WITHIN A 10 PERCENT UNCERTAINTY CN VU 

SUBROUTINE OATE 5/30/7D 



79 



TA3LE 5.7 
INTERFACE ELEMENT - THREE-DIMENSIONAL 
ELEMENT PP1N7CUT EXPLANATIONS 

NUM9EP OF 
LASEL CONSTANTS FORMAT EXPLANATION 

LINE i 

3-0 GiP 1 15 ELEMENT NUHSSP 

H03£5 2 2 IS NODES I AND J 

USE?»USLICECY,Z) 2 2F9.3 GAP SIZE. SLIDING CISTA.NCE IN LOCAL 

QIRECTTON» SLIDING DISTANCE IN L'OC 
Z OIRECTION 

KTY?5 1 12 INTERFACE CONDITION INOICATOP 

1 - RIGID CONTACT 

2 - SLIDING CONTACT 

3 - FREE 

KOLD 1 12 XTYPE VALUE OF THE PREVIOUS ITEPATIC 

LINE" ? 

FN 1 G14.6 NORMAL FORCE (ALCNo I-J LIME) 

F3 1 G14.6 TANGENTIAL FORCE (VECTOP SUM) 



80 



TABLE s.3 
ISOPARAMETRIC QUAOPILATEPAL TEMPERATURE ELEMENT 

SU3P0UTINE NAME STIF35 

NO. Or MOOES PEP ELEMENT - I»J»K,L 

DECREES GF FREEDOM PEP MOOS 1 TEMP 

REQUIRED REAfc CONSTANTS 

HEAT GENERATION RATES 1 AVERAGE 

CONVECTION SUP?" ACES ^ lJ»UX,.<L»Ll 

HA7E.PIAL PROPERTY ECUA7I0NS ^ XXX»KYY »OENS»C CGLC8AL) 

MATRICES CALCULATED CONDUCTIVITY, SPECIFIC HEAT 

KEYSU3<1> - PLANE 

1 - AXISYMMETPIC 

«EYSu3(lA) - INCLUDE EXT* A 7EHPEPA7URS SHAPES 

1 - SUPPRESS E~7RA TEMPERATURE SHAPES 

KEYSUS(2: - NO CONVECTION SURFACE PRINTOUT 

1 - PRINT OUT HEAT FLOW SATE FRO* 
CONVECTION SURFACES 

SVJSPOUTINE 0A7E 6/22/73 

7A8LE 5.9 
ISOPARAMETRIC GUACRILATERAL TEMPERATURE ELEMENT 
ELEMENT PRINTOUT EXPLANATIONS 

NUMBER OF 

LABEL CONSTANTS FORMAT EXPLANATION 

LINE i _ (PRINTED ONLY IF K£YSUS-(2) = 1) 

ELEMENT NUMBER 
CONVECTION FACE NOOES 

(I»J OR J*K OR ,K,L OR L»I) 

CONVECTION -ACE NUMBER 
CONVECTION SURFACE AREA 

AVERAGE FACE TEMP, FLUID SULK TEMP. 
HEAT FLOW RATE ACROSS FACE 

LINES 2>2»- (SAME AS ABOVE FOR OTHER CONVECTION SURFACES* IF DEFINED) 



ELEMENT 
NOOES 


1 
2 


15 
2IS 


FACE 

AREA 




12 

Fa.* 


TAVG.T3ULX 

HEAT FLOW 


2 

1 


2F6.0 
Gil. A 



81 



TABLE 5.10 
CONDUCTING BAR - TWO-DIMENSIONAL 



SUBROUTINE NAME 
NO. OF NODES PER ELEMENT 
DEGPEES OF FREEDOM PER NODE 
REQUIRED REAL CONSTANTS 
HEAT GENERATION ,RATES 
CONVECTION SURFACES 
MATERIAL PROPERTY EQUATIONS 
•MATRICES CALCULATED 
ELEMENT PRINTOUT 
SUBROUTINE OATE 



ST 


IF32 




2 


I,J 




1 


TEMP 




1 


AREA 




1 


AVERAGE 











3 


KXX.DENS.C 




CONDUCTIVITY .SPECIFIC 


HEAT 


NONE 




7/' 


01/70 





p M x M' 'A' 'X X' 'X 'Jfc *X J 



82 



TABLE 5.11 
TViO— DIMENSIONAL ISGPaflAHETRlC ELEMENT 



SUBROUTINE NAM? 
NO. OF NODES PES ELEMENT 
DEGREES 05" FREEDOM PER N02E 
REQUIRED PEAL CONSTANTS 

TENPFPATUnES 
PRESSURES 

MATERIAL PROPERTY EQUATIONS 



MATRICES CALCULATED 

PLASTICITY 

CREEP AND SWELLING 

FORCES SAVED CN TAPE 

KEYSua CD 
KETSuBClAJ 



STIFLE 

2 





1 

6 
10 



I»J*X»L (NUMBER CCUNTER-CLQCXylSE) 

UX*UY 

IF" KSYSUS(l) = 0.1.2 
THlCXNESS, IF XSYSU3U) » 3 



Til) ,TU> ,T(X) »T(L) 
PCI) »P<2> *P<3) »P-(*) 

IF PLANE STRESS - 
EX ,SY .NUXY , AL?X , AL?Y ,OENS 
GXY (OPTIONAL) 

IF AXISYM OR PLANE STRAIN - 
EX,EY»E2,.NUXY,NUY2.NUX2»AL?X,ALPY> 
ALP2»0ENS GXY (OPTICNAL) 



MASS ♦STIFFNESS 

YES 



NO 

26 



SIGMAX.SlGMIN.TAUMAX.SIG2.SIGc. 

E?GSN»SIGX.S I GY,TAUXY. TEMPERATURE. 
W ELASTIC STRAINS, \ PLASTIC STRAI 
4 0. SHIFT STRAINS, 4 THERMaL STRaI 



- PLANE STRESS 

1 - AXISYHMETRIC 

2 - PLANE STRAIN (2 STRAIN = 0.0) 

3 - PLASZ STRESS WITH THICKNESS INPUT 

- DISPLACEMENT FORMULATION INCLUDES THE 

EXTRA MOOE SHAPES 

1 - DISPLACEMENT FORMULATION DOES NOT 

INCLUOE THE EXTRA MOOE SHAPES 



(CONTINUED ON NEXT PAGE) 



83 



TABLE 5. IT 



(CONTINUED) 



<£YSuS(2} 



3 - 



t+ - 



NO SURFACE STRE33 PRINTOUT 

PRINT OUT STRESSES FOR SURFACE I -J 

PRINT OUT STRESSES FOR 30TH SURFACES 

I -J AND K-L 

(SURFACE STRE33 PRINTOUT AVAILABLE ONLY 

FOR ISOTROPIC. ELASTIC MATERIALS) 
PRINT OUT SOLUTION AT ALL INTEGRATION 

POINTS AS WELL AS AT CZNTROID (FOR 

PLASTIC SOLUTIONS ONLY. ADOS 15 MORE 

LINES ?Z? ELEMENT") 
PRINT STRESSES AT Th£ <+ NODES AS WELL 

AS AT CSNTROID (KEYSU8QA) MUST = 0) 



*£T5u3(2A) 



- PRINT SOLUTION A7 ELE.ME.NT CcNTROlD 

1 - REPEAT LINES 1 ANO 2 OF SOLUTION FOR 

ALL OTHER INTEGRATION POINTS (ACOS 
16 MORE LIN -13 PZri ELEMENT 1 



SUBROUTINE OATE. 



^/DO/72 



34 



TAfcLE 3.12 

t'wo-oi^ensicnal isoparametric et.shs.nj 
element printout explanations 



LAS£L 




NUHSE.R OF 
CONS 7 AN 7 3 


FORMA 7 


line i 










EL EM 
NODES 

vol 

MA7EP I A 
STRESS 
S 1 3 E.~F 


L 
IM" 


1 
4^ 

i 

1 

1 
I 




15 
415 
"1 .A. 

12 

"3.0 

F3.0 


LINE 2 










X 
Y 

i 

XY 3TR 




I 

1 
1 

4. 




F6.2 
F6.2 
F5.0 
4F 3 • 0- 


H.A^-T-»I*N 


1 S7 


R 3 




3F3.0 


A 




1 




F5.1 



EXPLANATION 



ELEMENT NUM5SR 

N00S3 I* J, X, A.NO L 

VOLUME Of ELEMENT 

MATERIAL NUM9ER 

STRESS INTENSITY IN THIS ELEMENT 

VON MIScS EQUIVALENT STRESS 



X. COORDINATE C? CENTROID OF ELEMENT 
Y C00R0INA7E Or CENTpOID OF ELEMENT 
AVERAGE 7EHPERA-uRE OF ELEMENT 
SIGx, SIGY, TAUxY. -NO SIGZ 

(SIG2=0.0 FOR PLANE STPE3S ELEMENTS) 
3IGHAX, SIGN IN, ANO TAUMAX 

(IN-PLANE PRINCIPAL STR£SS£3) 
ANGLE OF PRINCIPAL STRESSES RESTIVE TO 

7h£ GL03AL X-Y ±ZZ5 

LINE I -J SURFACE I -J STRESS CONDITIONS (PRINTED ONLY. IF KEYSU3<2> IS 

1 OR 2) 

AVERAGE TEMPERATURE OF I-J SURFACE 

ELASTIC SURFACE STRAIN COMPONENTS 

(PARALLEL* PERPENDICULAR* Z OR HOOP) 

ELASTIC SURFACE STRESS COMPONENTS 

(PARALLEL* PERPENDICULAR* Z OR HOOP} 

SURFACE STRESS INTENSITY, SU^f XCZ 
VON MISE5 EQUIVALENT STRESS 

LINE X-L SURFACE X-L STRESS CONDITIONS (PRINTED ONLY IF x£YSUS(2) = 2) 

-tSAHE AS LINE I-J.ASQVE 3UT APPLIED TO FACE X-D 

LINES 3 ANO 4 NON-LINEAR SOLUTION (PRINTED ONLY IF X13 IS GREATER THAN 

ZERO ON CARD CI) 

£?SL 4 4F10.7 ELASTIC STRAIN COMPONENTS CX,Y,XY,Z) 

EPPL - 4 4F10.7 PLASTIC STRAIN COMPONENTS (X,Y,XY,Z) 

LINE 3 NON-LINEAR SOLUTION (CONTINUED) 

eporig 4 4f10.7 shift of origin of stress-strain curve due 

70 Previous loao cycles 
spgen 1 f10.7 equivalent strain 

PC5G£N 1 F10«A EFFECTIVE P0ISS0NS RA7I0 

SIGE 1 F10.2 EQUIVALENT STRESS 

NOTE I - STRESSES AND STRAINS ARE PRINTED AFTER THE PLASTICITY CORRECTIONS. 

NOTE 2 - FOR AXlSYNMETRIC SOLUTIONS, THE X,Y,XY» AND Z STRESS ANO STRAIN 

OUTPUTS CORRESPOND TO THE RAOIAL, AXIAL, IN-PLANE SHEAR * AND HOOP 
STRESSES ANO STRAINS, RESPECTIVELY. 



T 
STRAIN 


1 

3 


F3.0 
3F10.7 


STRESS 


3 


3F3.0 




2 


2F9.0 



35 



TABLE 5.13 

INTERFACE ELEMENT - TJQ DIMENSIONAL 



SUBROUTINE NAME 
NO. OF NOOSS PZri ELEMENT 
CEGREE3 0?" rS£S30H PER NOQE 
REQUIRED REAL CONSTANTS 



TEMPERATURES 
P PES SUP £3 

MATERIAL PROPERTY EQUATIONS 

MATRICES CALCULATED 

PLASTICITY 

FCRCFS SAVED ON TAPE 

KEYSU8<1> 



<EYSti8<2) 



STIF12 

2 

2 



I.J 

UX»U7 

TH£TA*STIFFNESS* INTERFERENCE* START. 
A NEGATIVE INTERFERENCE ASSUMES AN 

INITIALLY OPEN GAP 
IT START = 0.0 OR 5LANX, PREVIOUS 

CONDITION CF SAP DETERMINED FROM 

INTERFERENCE 
IF START = 1.0* GAP PREVIOUSLY CLOS 

ANO NOT SLIDING 
IF START = 2.0. GAP PREVIOUSLY CLOS 

AND SLIDING RIGHT 
IF START => -2.0 » GAP PREVIOUSLY 

CLOSED ANO SLIDING LEFT 
IF START = 3.0» GAP PREVIOUSLY OPEN 

T(I) ,T(J) 



HU 



SUBROUTINE DATE 



STIFFNESS 

NO (NON-LINEAR ELEMENT) 

2 NORMAL FORCE(FN)» TANGENTIAL FORCECF 

- NO STIFFNE35 ASSOCIATED WITH SEPARATED 

INTERFACE 

1 - STIFFNESS»I.0E-<5 ASSOCIATED WITH 

NORMAL STIFFNESS FOR SEPARATED INTER 
FA.CZS AND WITH TANGENTIAL STIFFNESS 
FOR SLIDING INTERFACES 

- CONVERGENCE 3ASED ON UNCHANGING ElEME> 

STATUS 

1 - CONVERGENCE BASED ON CHANGING ELEMENT 

STATUS WITHIN A 5 PERCENT TOLERANCE C 
HU 

2 - CONVERGENCE 3ASED ON CHANGING ELEMENT 

STATUS WITHIN A 10 PERCENT TOLERANCE 
MU 

<*/0W72 



86 



TASLE 5.14 
INTERFACE. ELEMENT - TWO DIMENSIONAL 
. ELEMENT PRINTOUT EXPLANATIONS 



EXPLANATION 

ELEMENT NUH3E5? 
NOOES I ANO J 

GAP SIZE* SLIDING DISTANCE 
NORMAL FORCE 
TANGENTIAL FORCE 
ELEMENT STATUS 

1 - GAP CLOSED, NO SLIDING 

2 - SLIDING CONTACT (NOOE J MOVING TO 

RIGHT Or NOOE I) 
-2 - SLIDING CONTACT (NCOS J MOVING TO 
LEFT OF NOOE I) 

3 - GAP OPEN 

OLD 1 12 KlyPE VALUE" OF THE PREVIOUS ITERATION 





NUH8ER 


OF 




LA3FL 


csnsta.s 


iTS 


FORMAT 


EL EM 


1 




15 


NQOE5 


2 




2IS 


US£?,USLIDE 2 




2F9.S 


FN 


1 




G13.5 


FS 


1 




G13.5 


KTYPE 


1 




12 



87 



z 

I 




-^— Y 



MOTE - Surface stressas ara available on faces -2 and 4. 
(Surface coordinate system shewn) 



Figure 5.1. Three -Dimensional Isoparametric Solid Element 



Z 



M 




Figure 5.2. Three-Dimensional Isoparametric Solid Element Output 



88 




Figure 5.3. Three-Dimensional Interface Element. 



> 


I 




F n 


Slope = k/10 6 
if KEYSX3B(1)=1 






. ■ 




A* 


( u n)j-< u n)l + ' GAP 




/i 







"IN 




Slope=k/lO 
or* KEYSUB(l)=l 



T 

±5% tolerance 

if KEYSUB(2)=1 
>• 



(usJj-^sJj - USLIDE 



^I F «i 



for F < 
n 



Figure 5.4. Three-Dimensional Interface Element Output 



89 



(or Axial ) 




Q - Convection Face Numbers 



Heat flow out of the element is positive 



(or Radial) 



Figure 5.5. Isoparametric Quadrilateral Temperature Element 



90 



(or Axial ) 




->— X (or Radial) 



Figure 5.6. Two-Dimensional Conducting Ear Element 



91 



( or Axial 



£\ - Face Numbers 




Surface Stresses are 
available on Face 1 
and Face 3. 



X (or Radial) 



Figure 5. 7 . Two -Dimensional Isoparametric Element 



(or Axial) 




t*— X (or Radial) 



Figure 5.3. Two-Dimensional Isoparametric Element Output 



92 



Y 

ar Axial) 

I 



INTERFERENCE CONDITIONS I 




I *■ 



8 determines element 
orientation 



I * T(I) 
Nodes may be coincident 



(or Radial) 



■£ 1 5 »' 



S<° 



+-= •-— o 



-*}s>oh- 



RIGHT SLIDE 
(KTYPE OR START 
= +2) 



Figure 5.9. Two-Dimensional Interface Element 




SLOPE = k/10 6 
IF KEYSUB(1)=1 



c*,j.-<«v,) x -j 



Fl 



SLOPE = k/10 
IF KEYSUBI 



iYSUB(l)=l 2 




Cu,l -Cu,) x - 



usuioe 



- M\F^ ( 



For F« < O 



Figure 5.10. Two -Dimensional Interface Element Output 



93 



CHAPTER 6 
CONCLUSION 



The manual for ANSYS for analysts of anchored pavements has been 
prepared to provide the user a ready reference for analyzing the re- 
sponse of anchored pavement system subjected to vehicle static loads, 
moisture variation, and temperature variations. 

The manual is prepared so that it can be used with a minimum num- 
ber of references. For preprocessing, Chapter 3 provides the details 
of a program developed at I IT called FEMESH. The User's Guide for 
ANSYS has its own preprocessing subroutines, however, the FEMESH is 
more efficient for preprocessing the anchored pavement system. If any 
postprocessing Cpost-plotting) is desired, the User's Guide for ANSYS 
should be consulted. In the particular analysis performed, postpro- 
cessing was not utilized as plotting was done by hand. 

The computer program provides the numerical values of stresses, 
strains, deflections in all elements of various materials. There is 
no practical limit of restriction of material numbers, that is the 
program can be used with different materials in any direction. For 
heat transfer, the program provides the distribution of temperature 
versus time at any point. 

ANSYS in general has the capability of obtaining response of the 
pavement system under transient dynamic loads, however, this has not 
been incorporated in this manual. 

The most noteworthy point for the ANSYS program is the wave front 
solution and certain limitations caused by the said solution. The 
ordering of nodes therefore must be done to minimize the size of wave 
front as has been explained in detail in Chapter 4. The program has 
been found versatile and capable of solving complex geometrical struc- 
tures resting on complex geologically earth mass. 



94 



REFERENCES 



1. Bathe, K.J. and Wilson, E. L. , "Numerical Methods in Finite 
Element- Analysis," Prentice-Hall, Inc., (New Jersey, 1976. 

2. Cook, R. 0., "Concepts and Applications of Finite Element 
Analysis," John Wiley and Sons, New York, 1974. 

3. Desai, C. S. and Abel , J. F, , "Introduction to the Finite 
Element Method," Von Nostrand Company, New York, 1972. 

4. DeSalvo, G. J., "ANSYS Verification Manual," Swanson Systems 
Inc., 1976. 

5. DeSalvo, G. J. and Kohnke, P. C. , "ANSYS Introductory Manual," 
Swanson Analysis Systems Inc., 1975. 

6. DeSalvo, G. J. and Swanson, J. A., "ANSYS Examples Manual," 
Swanson Analysis Systems Inc., 1972. 

7. DeSalvo, G. J. and Swanson, J. A., "ANSYS User's Manual 
CRevision 2)," Swanson Analysis Systems Inc., 1975. 

8. DeSalvo, G. J. and Swanson, J. A., "ANSYS User's Manual 
CRevision 3)," Swanson Analysis Systems Inc., 1978. 

9. FORTRAN Extended Reference Manual, Publication Mo. 60497800, 
Control Data Corporation. 

10. Guyan, R. J., "Reduction of Stiffness and Mass Matrices," 
AIAA Journal , Vol. 3, No. 2, Feb. 1965. 

11. INTERCOM Reference Manual, Publication No. 60494600, 
Control Data Corporation. 

12. Irons, B. M. , "A Frontal Solution Program for Finite Element 
Analysis," International Journal for Numerical Methods in 
Engineering , Vol. 2, No. 1, Tan., p.p. 5-23, (Discussion May , 
1970, p. 149), 1970. 

13. Jones Jr., R. F. and Costello, M. G. , "A Solution Procedure for 
Nonlinear Structural Problems," . Numerical Solution of Nonlinear 
Structural Problems , ASME, pp. 157-169, 1973. 

14. Kohnke, P. C. , "ANSYS Theoretical Manual," Swanson Analysis. 
Systems Inc. , 1977. 

15. Kohnke, P. C. and Swanson, J. A., "Thermo-Electric Finite Elements," 
International Conference on Numerical Methods in Electrical and 
Magnetic Field Problems, Santa Margherita Ligure, Italy, June 1-4, 
1976. 



95 



16. Lekhnitskii, S. G. , "Theory of Elasticity of an Anisotropic 
Elastic Body," Hoi den-Day, San Francisco, 1963. 

17. Loader Reference Manual, Publication No. 60429800, Control 
Data. Corporation. 

18. Melosh, R. J. and Bamford, R„ M. , ''Efficient Solution of 
Load-Deflection Equations," Journal of the Structural Division , 
ASCE, Vol. 95, No. ST4, Proc. Paper 6510, pp. 661-676, 
CDiscussions, Dec. 1976, Jan., Feb., May 1970, Closure Fed. 
1971), April 1969. 

19. NOS/BE Reference Manual, Publication No. 60493800, Control 
Data Corporation. 

20. NOS/BE Users Guide, Publication No. 60494000, Control Data 
Corporation. 

21. Przemieniecki , J. S., "Theory of Matrix Structural Analysis," 
McGraw-Hill, 1968. 

22. Ralston, A. and Wilf, H. S., "Mathematical Methods for Digital 
Computers," John Wiley & Sons Inc., New York, 1962. 

23. UPDATE Reference Manual, Publication No. 60449900, Control 
Data Corporation. 

24. Wilson, E. L. , Taylor, R. L. , Doherty, W. P., and Ghaboussi, J., 
"Incompatible Displacement Models," Numerical and Computer 
Methods in Structural Mechanics , Edited by S. J. Fenves, et al . , 
Academic Press Inc., New York and London, pp. 43-57, 1973. 

25. Zienkiewicz, 0. C. , "The Finite Element Method in Engineering 
Science," McGraw-Hill Company, London, 1971. 



96 



APPENDIX A 
NOTATION 

The notation defined below is used throughout the appendices B and C. 



General 

Tzrzi Meaning 



[3] Strain-displacement matrix 

[C],[CJ Damping matrix, thermal damping matrix 

[D] Stress-strain matrix 

E Young's modulus 

{F} Force vector 

[K],[K] Stiffness matrix, conductivity matrix 

[H] Mass matrix 

{Q} Heat flow vector 

{T> Temperature vector 

[T R ] Local to global conversion matrix 

u,v,w,{u} Displacement, displacement vector 

dtl Virtual internal work 

6V Virtual external work 

x,y,z Element coordinates 

X,Y,Z Nodal coordinates (usually global cartesian) 

a Coefficient of thermal expansion 

z Strain 

v Poisson's ratio 

c Stress 



97 



Superscripts and Subscripts on [ML ("CL'TO, (u>, {T}, and/or (F) 

No subscript implies the total matrix in final form, ready for solu- 



ti on . 



a nodal effects caused by an acceleration field 

c convection surface 

cr creep 

e based on element in nodal coordinates 

g internal heat generation 

l based on element in element coordinates 

Id large displacement 

m master 

n nodal effects caused by externally applied loads 

pi plasticity 

pr pressure 

s slave 

sw swelling 

t thermal 

— (bar over term) heat transfer matrices 

(flex over term) reduced matrices and vectors 

(dot over term) time derivative 



98 



APPENDIX 3 
ANALYSIS PROCEDURES 

This section of the manual is designed to give users an understanding 
of the theoretical basis of each analysis type. The derivation of the individual 
element matrices and vectors is discussed in Appendix C. 

In the matrix displacement method of analysis based upon finite element 
idealization, the structure being analyzed must be approximated as an assembly 
of discrete structural elements connected at a finite number of points (called 
nodal points). If the force-displacement relationship for each of these dis- 
crete structural elements is known (the element "stiffness matrix") then the 
force-displacement relationship for the entire structure can be assembled using 
standard matrix methods. 

Figure Bl gives a summary of the ANSYS analysis procedures available 
and may be used as a guide in selecting which type to use. Each of the 
analysis procedures is described in the following sections. 

STATIC ANALYSIS 

The overall equilibrium equations for static analysis' are: 
[K]{u> = {F} (B.l)' 

N 

where: [K] - total stiffness matrix - Z [K ] 

m=l e 
{u} = nodal displacement vector 

N - number of elements 

C'O = element stiffness matrix (may include 

the element stress stiffness matrix^ 

99 



f start) 




TRANSIEHT AND 

STEADY STATE 
THERMAL ANALYSIS 



SUCKLING ANALYSIS 

(:<a,n-t) I 



NON-LINEAR 
TRANSIENT DYNAMIC 

ANALYSIS 

C<AN»<M 



REDUCED LINEAR 
DYNAMIC TRANSIENT 
ANALYSIS 
(JCAN-S) 



HARMONIC RESPONSE 
IS 
(XAN-3) 



^-ANALYSIS 



REDUCED HARMONIC 
RESPONSE ANALYSIS 
( KAN-6 ) 



MODE FREQUENCY 
- ANALYSIS 
(JCAN-2) 



<AN is tha '<ay input on tha CI card to select the analysis type 
Quasi -Linear - the only non-linearities peraittad ara caps. 



Figure Bl. Summary of ANSYS Analysis Types 



100 



{F}, the total force vector, is defined by: 

•{F} = {F n } + (F a ) + Z ({F*}-+ (Ff > + {F? 1 } + {Ff } 



+ (Ff } + {Fl d » (3.2; 



e a 



where: {F } = applied nodal load vector 

{F } = [M]{A } = acceleration load vector 

N 

[M] s total mass matrix 2 [M ] 

m=l a 

[M ] - element mass matrix 

{A } = nodal acceleration vector 

(FT = element thermal load vector 

e 

{F^ } = element pressure load vector 

CF? } = element plastic strain load vector 
e 

{F } - element creep strain load vector 

{F } = element swelling strain load vector 
e 



{F } = element large displacement load vector 



The same definitions used here apply to all other analysis procedures except 
heat transfer analysis. 

If sufficient boundary conditions are specified on {u} to guarantee 2 
unique solution, equation 3.1 can be solved to obtain the nodal point dis- 
placements at each node in the structure. The simultaneous equations with all 
degrees of freedom (including those with specified displacements) are given in 
equation 3.3. 

101 



:< 


K 

r 


<r T 


K rr 



/ 



> 



r \ 



F. 



V 



(B.3) 



L J 



The subscript r is associated with the reaction forces. Mote that {u } 

H 

is known, but not necessarily equal to {0}. The top half of equation 
3.3 inay be solved Tor' luj-r 



{u} .= -[;<]- '[^{u^ + [K]"'{F} 



The reaction forces {F } may then be computed from the bottom half of 
equation 3'. 3 ; 



(F r > » c^fcu} + [;< rr ]{u r > 



(B.5) 



These reaction forces should always be in equilibrium with the applied 
loads. The following circumstances could cause a disequilibrium, usually 
a moment disequilibrium: 

1. The presence of stress stiffening 

Mote that moment equilibrium is not preserved/ 
•"Hits may. be accounted for as as 
implicit updating of the coordinates. 

2. Tne presence of four-noded shell elements where the 
four nodes do not lie in a flat plane. 

3. The presence of nodal coupling or constraint equations. 
The user can write any form of relationship between the 
displacements, and these may induce fictitious forces or 
moments. Thus, the reaction force printout has been used 
to detect input errors. 



102 



1.3 HEAT TRANSFER ANALYSIS (KAN=-1) 

Steady stats and transient heat transfer problems may be solved by 
finite element techniques analogous to those used for structural analysis. 

A. Steady State 

The basic thermal equilibrium equation is: 

ro<T}.--tQ) (B.6) 

where: [K] ■ thermal conductivity matrix 

-CQ} = heat flow vector 

{T} - vector of the nodal point temperatures 
This equation is identical in form to equation B.l for static analysis. 

If the material properties and film coefficients are not temp- 
erature dependent, equation B.6 can be solved directly with one 
iteration. If the material properties (or film coefficients) are temper- 
ature dependent, they are evaluated at the temperature of the previous 
iteration. The procedure used is shewn in Figure B2. 

An optional convergence criterion is available with steady- 
state analysis. All nodes are monitored for the largest change in temp- 
erature. If this largest change is less than the criterion,, then the 
solution is said to be converged. This criterion is input on the MD card 
(TCV) and defaults to 1.0 degree. 



103 



(Stjrt) 



Set all 

temperatures equal 

t0 T UNIF (l ' nput 
quantity) 



Evaluate [1] p- 4 



i 



Solve for {7} 




Figure B2. 



Flow chart for Steady State Heat Transfer 
Analysis with Temperature Dependent 
Material Properties. 



B. Transient 



The basic thermal diffusion equation is: 
[C]{T } + [K]{T} = {Q} 
where [C] is the specific heat matrix. 



(B.7) 



104 



The form of this equation is .identical to the non-linear dynamic 
transient equation (KAN-4) except that the mass term is not present. For 
temperature dependent material properties (or film coefficients), the eval- 
uation of the properties is made at a temperature extrapolated from the 
previously calculated temperatures. 

The time-integration schemes are also the same as that of the non- 
linear transient dynamic analysis type (KAN=4) except that the options 
offered are one order lower, i.e., linear (KAY(2)=2) and quadratic (KAY(2)=0 
or 1, the recommended usage). The linear (first order) equation is: 

(^-[C] +'TO){T t > = {Q(t)> + CC]{T t-1 ) ^- (B.3) 

The quadratic (second order) equation is: 



( 



2At n + At, t 

-St^^Cc] + raja t > = (Q(t) ) + 



where: t Q ■ present time 
t, = previous time 
t~ = time at second previous time 

At, - V fc 2 

T, ■ temperature at this time step (to be calculated) 
T. , = temperature at previous time step (known) 
T t 7 - temperature at second-previous time step (known) 



105 



The starting procedure of the transient thermal analysis is as 
follows: If the first load step is run at time = 0. (TTME=0. on L card), a 
steady-state analysis is performed at that time. Alternatively, if the first 
load step is run at time > 0. (TIME > 0. on L card), all temperatures at 
time = 0- are set equal to TUNIF. The temperatures at time = £, (t. means 
the solution at time i) are determined by the user selected time interpret- 
ation procedure- (linear or quadratic, depending on the value of KAY(2J). If 
the quadratic integration is used, it is started by setting all temperatures 
at a previous time point (t ,) to those values at time = 0. 

It is not recommended that the time step size between adjacent 

d 2 J 
iterations be changed by more than a factor of ten, unless — j is very 

• d-T 

smal 1 . 

An option is available to increase the time step size automatically 
if the rate of change of temperature at all nodes is less than an input 
criterion. This optimization criterion is input on the MD card as TOY, which 
defaults to 5.0 degrees. Using the default value, this criterion may be 
expressed as: 



max 



d*T ,.2 

d-r 



< 5, 



(3.10) 



Because a history has to be developed, the time step size may be increased 
only after the second iteration. 



106 



APPENDIX C 

ELEMENT LIBRARY 

Each element In the ANSYS program is discussed in this section. The 
assumptions required to generate the element matrices and load vector are 
given,, including the assumed shape functions. Certain aspects are also dis- 
cussed' in the chapters on the nonlinear capabilities of ANSYS. Elements with 
nonlinear material properties (plasticity, creep, and/or swelling) have appro- 
priate quantities saved at the integration points, except as noted. 

In broad terms, all stress and thermal elements have their appro- 
priate matrices and vectors derived using the procedures in the following two 
sections entitled: 

Virtual Work Derivation for Stress Analysis Elements. 

Virtual Work Derivation for Thermal Analysis Elements. 

These derivations assume the use of an isoparametric element* as that element 
family is one of the simplest. On the other hand, a complete virtual work 
derivation is also given with elements STIF46, STIF53, and STIF61 , which are 
not isoparametric elements. 

Virtual Work Derivation for Stress Analysis Elements . 

The principle of virtual work says that a virtual (very small) 
change of the internal strain energy must be offset by an identical change 
in external work due to the applied loads, or: 

6\J = 5 V (C.l) 

where: $ u = virtual strain energy (internal work) 
5 V ■ virtual (external) work 



107 



"he virtual strain energy is 



{o-} 1 {a} d(vol) 
vol 



(C.2) 



where: {s } = strain vector 
{a} - stress vector 
vol = volume of element 

The stress is related to the strains by: 
M = [D](u> - { £th }) 



(C.3) 



where: [D] = material property (constitutive) matrix 
te+u} ~ thermal strain vector 



Equation C,3 ' may also be written as 



(s}= a th ) + [orV) 



(C.4) 



For the case of three-dimensional solid elements, equation- (2.0.4) may 
be exoanded to: 



r ~\ 




r ^ 


£ x 




V T 


£ y 




a AT 

y 


S z 


V _ J 


a AT 



Y 

xy 


r ~ ] 





y 
xy 







V 

At 







V. -/ 




^ J 



y + 



E 



-? r 







xy xz 

\- - f^- 

E y E z 



_^x ™ i Q 

E y u z 



; xy 







1 



~— 

G yz 



Q 



1 



xz 



< 



V (C5) 



xy 



'yz 



T xz 



108 



/■/here AT - the difference at the point in question between its own temperature 
and the reference (strain free) temperature (TREF). 

The [D] matrix is presumed to be symmetric, so that: 



J£X s _X£ 

E x E y 



(C.fi) 



ZX _ XZ 



(C7) 






(C.3) 



Thus, in terms of ANSYS input variables: 



[D] 



-1 



1 

EX 


NUXY 

EY 


NUXZ 
EZ 











NUXY 

EY 


1 

EY 


NUYZ 

EZ 











NUXZ 
EZ 


NUYZ 
EZ 


1 

EZ 




















1 

GXY 




















1 

GYZ 




















1 

GXZ 



(C.9) 



and: 



{£ th> 



= < 



'alpxutP 

ALPY(aT) 
ALPZ(aT) 







> 



(CIO) 



109 



If GXY, GYZ, and GXZ are not input, they are computed as 



rvv - ^X EY (r in 

Ga/ " £X + £Y + 2 NUXY EX l j 



G7Z S £Y + £Z + 2 NUYZ £Y (C ' 12) 



GXZ S cv , C->" ■ % UIIV-7 -V ( C . I 3 , 

EX + t£ + 2 NUXZ cX 



A further comment on the [D] matrix: It must be positive definite. 
This condition is always met if the material is isotropic or NUXY, NUYZ, 

and NUXZ are all zero. But, for example, if EY is less than c-r equal to 

2 
EX (NUXY) , the material is not positive definite. 

{e- ) may also be considered to include plastic, creep, and 
swelling effects, where applicable. 

Equations C.2 and C.3 are combined to give: 

<5U = J ({6£} T [0]{£> - {o£} T [D]{ £th » d(vol) (C14) 



-'vol 



The strains may be related to the nodal displacements by: 

U> - CB]{u} (C.15 

where: [B] - strain-displacement matrix 

{u} - nodal displacements 
Combining C.15 with C. 1 4 ., and noting that {u} does not vary 
over the volume: 



<5U =-(u} T 



[3] T [0][3j{u} d(vol) 



vol 



- (u} T f [3] T [0]U th } d(vol) (C.16) 

vol 

110 






Next, the virtual work will be considered. The inertia! effects 
will be studied first: 

«V-I {Sw^UfVvoI)} d(vol) (C.T7) 

J vol 

where: {w} « vector of displacements of a general point 
{r } ■ acceleration (D'Alembert) force vector 

According to Newton's second law. 

7or = PiT {W} . «-T8> 

where: p - density 

t ■ time 

The point-wise displacements are related to the nodal displace- 
ments by: 

w - [A] u (C.19) 

where [A] - matrix of shape functions. Combining equations 
C.18 and*CiT9": 

5V = {5u} T p I [A] T [A] d(vol) Wu} (C20) 

-/vol 3t 

The pressure force vector formulation starts with: 

5V = I {5w} T {p} d(area) (C.21) 

-' area 

where {p} - the applied pressure vector (normally contains only one 
non-zero component). 



Ill 



Combining equations 

5V = {6u> T f [A] T { P } d(area) (C.22) 



area 



Finally, equations 
combined to give: 



{5 a} 7 [3] T [D][3]{u> d(vol) 

Jvol 

- (3u} T [3] T [0]{s: th } d(vol) 

^YOl 



- {ou} T p [A] T [A] d(vol) |r {u} 

+ {<5u 7 }p J [A] 7 d(area) (C.23) 

-* area 

Noting that the {00} is common in all of the above terms, and that its 
terms are independent of each other, it may be cancelled out. Thus, 
equation C.23 reduces' to":""' 

DC e ]{u} - {F^} = [M e ]{u> + {?l r } (C.24) 

where: [K ] = I [B] [D][B] d(vol) = element stiffness matrix 
e Jvol 

ir } * I [3] [0]{£^u> d(vol) = element thermal load vector 

e J vol * 

[M«] = p I [A] [A] d(vol) = element (consistent) mass matrix 

' e J vol . 

.2 
{u} =fr-{u}= acceleration vector (such as gravity effects) 

a U 

ny I T 

{F* } - [A] {p> d(area) = element pressure vector 
J area 



112 



Those elements which use a lumped sum mass matrix rather than a consistent 
mass matrix are noted with the individual element description. 

The element stresses are computed by combining equations C.3 
and c.15 to jet: 



M - CD]([B]{u} - { £th » 



(C.25) 



Mote that [S] is the strain-displacement matrix that must be specialized 

for each stress calculation point (centroid, integration point, node point, etc,} 

Virtual Work. Derivation for Thermal Analysis Elements 



As before, the basic expression of virtual work is: 

SU = sV 

where: 511 = virtual internal work 
5V s virtual external work 

In thermal terms, the virtual work within one element is: 
<5U 



(C.26) 



- I (5S> T 

-'vol 



{Q v > d(vol) 



(C.27) 



where: 



C 



3T(x,y,z) 



ax 



(S>< J 3T(x,y, 2 ) 

3T(XvY,z) 



> - vector of temperature 



v 



3Z 



IP 

s x 



WJ=< 



> = vector of heat flows 






v. Q «J 



113 



7(x,y,z) = temperature at point x,y r z 

Q = heat flew in the x-di recti en per unit area 
Q- = heat flew in the y-di recti on per unit area 
Q_ = heat flew in the z-di recti an per unit area 



The heat flows are related to the temperature gradients by: 



wnere: 



<Q.,i ■ 


[0]{S} 
















[D] - 





KYY 







, 





KZZ 



(C.2S-) 



The temperature distribution within an element is based on the assumed 
temperature shapes: 

T(x,y,z) = (M}'{T } 



(C.29, 



where: {N} = vector of shape functions 

{!'} = nodal temperature vector 
e 



Then, {S} is related to {7 } using the definition of {S> and equation 
C.29 to give: 



{S} = 



[3]{T e > 



(c.3a) 



wh 



ere 



[B] = 



{— } 



T 



l 3y ' 



T 



T 



{ iN } 
l 3X ; 



Combim'na ecuations ■ C.27, C.28, and C20 and realizing that 



114 



the nodal temperature vector does not change over the volume of the 
element, 



? r [b] t i 

Jvol 



«U s {ST.}' [B]'CD][B] d(vol) {T } (C.31) 

e Jvol e 

Next, consider the virtual internal work associated with con- 
vection surfaces: 



..] 



5AT Q d(area) (C.32) 

area 



where n = :i the direction normal to the surface. AT is defined by: 



AT = T(x,y,z)| - T B (C.33) 



where: T(x,y,z)| - the temperature function evaluated at the 

s 

convection surface 

T„ s temperature of the coolant (bulk temperature) 



Note that T„ is a constant so that 

SAT -«T(x,y,z)| (C.34) 

s 

The heat flow over the unit area is defined by: 

Q n = h f AT (C35) 

where h f = film, coefficient for heac. transfer of the surface. Combining 
equations C.29, C.32, C.33, C.34, and c.35, and noting that {T g } does 
not vary over the surfaced arid that Tg and h f are. assumed not to: 



115 



oU*{oT e } T h f 1 {N| } T d(arga)-{T e > 
area s 

-C5T e > T h f T 5 f {N| > d(area) (c.36) 

-/ area 

where {N| } are the shape functions evaluated at the convection surface, 
s 

The internal heat generation rate effect is included by con- 
sider? na: 



5V -- J oT(x,y,z) q d(vol) (C.37) 

where "of = the heat generation rate per unit volume. Combining equations 
C.29 and C.37 and real vz4"ng- that the nodal temperatures vector (T } 
does not change over the volume of the element, and assuming that of 
does not chance over the volume of the element, 

5U={dT 8 > T q j {N} d(vol) (C.38) 

J vol 

The virtual internal work associated with a change of stored 

energy is: 

5U = I 5T(x,y,2)y d(vol) (C.39) 

-'vol 

3 T f x v 7 ) 
where: y = pC — ' lV~ ! -• total heat change per unit volume per 

P 3 C 

unit 'time 
p = density 
C = specific heat 
t = time 



116 



Combining equations C.29 and C.39 and noting that {T } does not vary 

over the element, and assuming that p and C do not vary over the 

P 

element, 

oU = (6T e } T pC p J 

vol 



oU = (6T e } T pC p J (N}{N} T d(vol) {t a } (C.40) 



where { y = ^ ty 

The effect of the nodal heat flows may be considered by, 

5V » (oT e } T {Q e ) (C.41) 

where {Q } is the nodal heat flow vector. 

Combining equations C.26, C.31, C.36, C.38, C.40, and C.41, 

and noting that since {<5T } is an arbitrary set of virtual temperature 
changes which may be cancelled out, 

[K a ] + [K^] (y + [Cj{y = {Q^} + {Qp + {Q e } (C.42) 

where: [K fi ] = J [B] T [D][B] d(vol) 

70 = total element conduc- 

[K?] = h f f (NL HNL } T d(area) tivity matrix 
e T y area 

[C ] ■ PC J {N}{N} T d(vol) = specific heat (thermal 
e " vol damping) matrix 



{Q e } = h f T BjT {N I S } d ( area ) 



area 



= total element heat 



rn q, ••• r ,.,, ,/ ,x flow vector 

CQ«} = q / {N} d(vol) 

e Aol 
This is the final temperature heat flow equilibrium equation. The 
above definitions are used to develop the element matrices and vectors 



117 



■ STIF12 - TWO-DIMENSIONAL INTERFACE ELEMENT 

The displacement functions for the interface element can be sep- 
arated into the normal and tangential directions because they are basically 
independent. 

Tn the normal direction, when the normal force (F ) is negative, 
the interface remains in contact and responds as a linear spring. As the 
normal force becomes positive, contact is broken and no force is trans- 
mitted; unless KEYSUB(1)=1 , in which case asmall force is supplied to 
prevent a portion of the structure from being isolated. 

In the tangential direction, for F < arid the absolute value 

of the tangential force (F ) less than or equal to (p|F |), the interface 

does not slide and responds as a linear spring in the tangential direction. 

However, for F„ < and F > u|F I , sliding occurs. Note that F„ is a 
n s ' n 1 s 

variable and if contact is broken, the tangential function degenerates 
to a zero slope straight line through the origin Cor of slope K/10 , if 
KEYSUBO)=l) indicating that no Cor little) tangential force is required 
to produce sliding. These may be related to each other by y|F | * 

K(u - u - u , . . A where u .. . is the distance of sliding. Figure 
s, s, slide) slide 

C2 shows ■" the; force-deflection relationships for this element. 




Figure CI . 



118 




SLOPE-* K/10° 
If KEYSUB(l) = 1 j) 

L 



(«„} - («„) - 4 



:» 



ulF. 



SLOPE =■ K/10 
If KEYSU3(1) = 1. 






1 




(O - (u ) 

s J s I 



-U r 



For F < and for 
n 



initial loading 
Figure C2. STIF12 Force-Oeflection Relations 

STTFI2 may have one of three conditions: in contact and not sliding, 
in contact and sliding, or open. The following matrices are derived with the 
assumption that 9 (theta) is input as 0.0. 



1. In contact and not sliding - The resulting equilibrium 
equation is: 



L 



K 





-K 





K 





-K 





K 





-K 






stiffness matrix 





-K 

K 



U s,I 



'n.I 



r sl 



nl 



r *\ 

" Ku o 



-KA 



<i r a -s f + i r (c ' 43) 

n 



's,J 



^ n,Jj 



sJ 

n 

nJ 



Ku. 



KA 



Displace- Applied Element Load 
ment Nodal Vector 
Vector Force 
Vector 



119 



where 



K = 

A = 

F = 
n 



input stiffness 
interference 
normal force across gap 

distance that nodes I and J have slid with respect to 
each other 



2» In contact and sliding - In this case, the element equilib- 
rium equation is: 



K -K 



-K K 

Stiffness Matrix 



r, 



< 



's,I 



l n,I 



's,J 



si 



>=< 



vVi 



nl 



sJ 



uF. 



F n 
I. nJ 



-KA 
-pF r 
KA 



Displace- Applied Element 
ment Vector Modal Load Vector 
Force 
Vector 



where y = coefficient of friction. 



(C.44) 



3. Open - When there is no contact between nodes I and J, the 
stiffness matrix and load vector are null matrices. 

The stress pass of STIF12 always uses the latest possible informa- 
tion concerning gap status. Therefore, for non-cnnverged iterations, it 
may not agree with the reaction forces which are based on the previously 
calculated stiffness matrix and load vector. 



120 



STTF32 - 2-0 CONDUCTING 3AR ELEMENT 

The temperature function is a linaar polynomial of the form: 



T(x) = C 1 + C 2 ; 



(C.45) 



wn 



ere the element x-axis extends along the element axis 



STTF42 - 2-0 ISOPARAMETRIC SOLID ELEMENT 

The 'displacement shape functions are repeated here for convenience, 
A local: coordtnats-s&sSem fs developed as shown -in Figure C3: 



Y.v 



(-1,1) 




(1,1) 



(-1,-1) 



(1,-D 



X,u 



Figure C3. Local Coordinate System 



121 



It is seen that s and t vary between -1 . and +T. The basic, isoparametric 
shapes yield the following set of shape functions: 

U b (s,t)- = 1(1 - S)(l - tJUj + ^{1 + S)(l - t)Uj 

+ \0 + s)0 + t)u ;< + Itf - s}(l + t)u L (C.46) 

v b (s,t) = 1{1 - s)(l - t)Vj + 1(1 + S)(l - t)Vj 



. 1 



1/, 



^■0 + s)(i + t)v ;< -i(i . sjq + t)v L 



(C.47) 



Mote that these shapes do not permit the edges to bend. 
The extra (and optional) shapes are defined as 

u e (s,t) = (1 - s^Cj + (1 - t 2 )c 2 

v e (s,t) = (1 - s 2 )c 3 + (1 - t 2 )c 4 



(C.48) 
(C.49) 



Their effect may be seen in Figure C4. c, through c, may be referred 
to as node! ess variables. The total displacements are then: 



u - u. + u 
d e 



v - v b + v e 



(C.50) 
(C.51) 




Without extra shapes 




With extra shapes 



fi- 



gure C4. Effect of Extra Shapes 
122 



These displacement shapes are used to' generate a 12 by 12 stiffness 
matrix. This matrix is then condensed to an 3 by 3 matrix, because there 
are only 3 decrees of freedom to connect to the rest of the structure- The 
condensation is analogous to that associated with superelement generation. 
The Toa <j vector "is also generated .with- TZ. terms and. is then: condensed to a. 
The mass matrix Ts consistent and is' generated as an- 8.. bf.£- 

A 3 by 3 lattice of integration points is used with the numerical 
(Gaussian) integra-tion procedure. 

Note that the extra shapes permit a parabolic deformation along an 
element edge. Normally this is helpful in modeling a structure, but 
occasionally it may cause a problem because of the incompatibility at the 
adjoining edges of two different elements, i.e., a gap opens up or the 
material "doubles up". The usage of the extra shapes is discussed in greater 
detail in the User's Manual. The extra shapes are automatically deleted if 
nodes K and L are the same (i.e. a triangle). This case then gives the same 
results as a constant strain triangle. 

The centroidal, integration point, and node point stresses' are com- 
puted by the procedure described at the beginning of this chapter (£quaticn c. 25 •] 

Surface stresses may be requested for elastic isotropic materials. 
Even though the development given below includes some orthotropic effects, 
it is only valid for a few special cases of orthotropic materials. The 
surface stresses for plane stress applications, are calculated by: 

1. Computing the strain parallel to the fr^e surface: 

u '- 

U T - u , 

I L x \C.zZ) 

123 



Where: u s displacement parallel to the free surface 
L = distance between the two surface nodes 
a * coefficient of thermal expansion (ALPX) 
AT s difference between average surface temperature and the 
reference temperature. 

2. Setting the stress normal to the surface (a-) to the applied 
pressure. 

3. Setting the stress in the z direction (a-) to 0. 

4. Solving for the remaining three quantities of interest 

(e 2 , £-, a, ) by use of the material property relationships. Specifically: 

°1 " e l h + v xy °2 (C - 53) 



6 3 = " v xy (ff l + ff 2 )/E ; 



(C.54) 



e 2>('2- u xy e l )/E a {C - 55) 

where: E, = (E, + Ej/2. 

a A j 

E = Young's modulus in the* x-di recti on (EX) 

E = Young's modulus in the y-direction (EY) 

v - Poisson's ratio (NUXY) 
*y 

For the axi symmetric option, steps 1 and 2 above are the same. 
Continuing, 

3. Computing the hoop strain (£3): 



T T T 

U T + U J % 



124 



where: u, = radial displacement of node I 

u, = radial displacement of node J 

u g - radial displacement of the midpoint of side I- J due to the 
applicable extra shape function 

R s radius of the midpoint of side I- J 

a^ s coefficient of thermal expansion in hoop direction (ALPZl 

4. Solving for the remaining three quantities of interest (e^* a i » 
a-) by use of the material property relationships. Specifically, 

a - £ 3 E z+ ( V+"xz v xy )q 2 + £ fxz E a (C.57) 

3 1 '* 



E. 
-it 



a, s £, E. + a„v + a-,v -f— (C.58) 



« =!i- v !l- v !i (C.59) 

e 2 E a u xyE a VE 2 



where: E s input quantity (E2) 



v ■ input quantity (NUX2) 
v = input quantity (NUYZ) 



Plane strain analysis is the .same as axisymmetric analysis,, 
except that step 3 is modified so that simply, 

e 3 = -a AT (C.60) 



125 



STIF45 - 3-0 ISOPARAMETRIC SOLID ELEMENT 

The element formulation includes incompatible displacement 
modes. A complete description of this technique is the three-dimen- 
sional extension of STIF42. Either a 3x3x3 or a 2x2x2 lattice of 
integration points is available for use with the numerical (Gaussian) 
integration procedure. For nonlinear material properties (plasticity, 
creep, or swelling), a 2x2x2 lattice is automatically used. 

The principal stresses are calculated from the cubic equation: 



x xy 



T xy a y ' a 



'xz 



yz 



T xz T yz a 2 ~ a 



= 



(C.61) 



The three computed values of a are the three principal stresses 



126 



STIF52 - 3-0 INTERFACE ELEMENT 

The Toad-deflection relationships for the interface element can be 
separated into the normal and tangential directions since they are basically 
independent. In the normal (element x) direction, when the normal force (F ) 
is negative, th& interface remains in contact and responds as a linear spring. 
As the normal force becomes positive, contact is broken and no force is trans- 
mitted (unless- KEYSU3(1 )=1 > then a small force is supplied to prevent a portion 
of the structure from being isolated). 

In the -tangential directions, for F < and the absolute value of 

n 

the .tangential force (F ) less than or equal to (y|F |), the interface does 
not slide and responds as a linear spring in the tangential direction. How- 
ever, for F < and F > ^ilF I, sliding occurs. Mote that F is a variable 
n s ' n ' n 

and if contact is broken, the tangential function degenerates to a zero slope 
straight line through the origin (or of slope k/10 , if KEYSUB(1 )=1 ) indi- 
cating that no (or little) tangential force is required to produce sliding. 
Figure CS shows' the* force- deflection functions" for this element- 



F nA 




Sloce=k/10° 
if KEYSUBOH 



(u n )j-(u n ) I+ GAP 



F s* 



y|F ! -- 




Slope=k/10 Q 
(if :<EYSUB(1) = 1 






±5% tolerance 
if KEYSU3(2)=1 



< u s>j-< u s>i 



--u F. 



for F < 
n 



.5''' 



Fiaure Co. 



Force-Defl ection Rel ationships 
127 



STIF55 - 2-0 ISOPARAMETRIC HEAT CONDUCTING SOLID ELEGIT 

The temperature functions used in STTF53 are a scalar form of 
those developed for displacements in STIF42. 
First, an element coordinate system is developed as shown in Figure Co. 



Y 
i 



(-1,1) 




(1,1) 



.(1,-D 



(-1,-1) 



Figure C6~. 



Element Coordinate System 



It is seen' that s and t vary between -1. and +1. The basic isoparametric shapes 
yield the following set of temperature functions: 



T. Q (s,t) = l/4(l-s)(l-t)T r + l/4(l+s)(l-t)Tj 
+ l/4(l+s)0+t)T K + l/4(l-s)(Ut)T L 

The extra (and optional) shapes are defined as: 
T e (s,t) = (l-s 2 ) Cl + (l-t 2 )c 2 



(C.52) 



(C.63) 



128 



C-, through c- may be r*farr*d to as nodal ass variables. The total 
temperatures are then: 

T = T. + T ( c - 64 i 

d e 

These displacement shapes are used to generate a 5 by -5 
stiffness matrix. A 3 by 3 lattice of integration points is used with 
the numerical (Gaussian) integration procedure. This matrix is then 
condensed down to a 4 by 4 matrix, because there are only four nodes to 
connect to the r^st of the structure. The condensation is analogous to 
that associated with superelement generation equation,' The load 
vector -is generated also with six terms and is then condensed down to 
four. The damping ( specif icfheat) matrix -is consistent and is also 
reduced down from a 6 by.-.-&.ta.aw4-by 4. 



129 



APPENDIX D 
COMPUTER DEFINITIONS AND COMMUNICATION LINKS 

DEFINITIONS (UNIVAC 1100 COMPUTER) 

The hardware organization of the 1110 (1100/40) and 1100/80 
Systems differ from that of the 1106, 1108, 1100/10, and 1100/20 
Systems. In some instances, different terms have been adopted for 
functionally similar components. In such cases, to avoid confusion 
and improve readability,, the 1108 term has, as a general rule, been 
used throughout this document synonymously with the corresponding 
1110 term, except where specific comments are made to the contrary. 
11 08- type will be used to include the 1106, 1100/10, 1100/20, and 
1108. 1110- type will be used to include the 1110 and the 1100/40. 

The principal corresponding terms are: 



1108 
CPU 
ACU 
Control 

Introductory 


Registers (■ 
Definitions 


bit 




Binary digit. 
value or 1 . 
the functional 



CICR) 



mo 


1100/80 


CAU(plus IOAU) 


CPU(plus 


SPU 


STU 


CRS 


GRS 



IOU) 



The fundamental unit of storage having the 
Bits are grouped in bytes and words to form 
manipulative units of storage devices. 

byte A group pf adjacent bits usually operated upon as a unit; 
can be 6, 9, 12, or 18 bits. 

buffer On 1100/80 a high speed storage interface (4k to 16k). 
storage 

Executive The 1100 Series Executive System. A program that controls 
or EXEC the execution of other routines. The Executive is the 
principal interface between the user and the system as a 
whole. It protects against undesired interaction of users 
with each other or the operating system. 

hardware Physical equipment, in the form of mechanical, magnetic, 
electrical, or electronic devices, as opposed to software. 

I/O Input/Output. The process of transferring information be- 
tween the central processor and peripheral, devices. I/O 
devices include: magnetic tapes, magnetic disks, magnetic 
drums, CRTs, card readers, printers, and punches. 

mnemonic Word or term devised so as to aid the human memory. Includes 
acronyms, such as TTY (telety pewriter) and error mnemonics, 
such as PWRLOS (powerloss). 



130 



operating The 1100 Series Operating System. The entire set of system 
system software available for the 1100 Series which is either a 
part of or operates under the Executive system. This in- 
cludes the Executive system proper, compilers, utility 
programs, subroutine libraries, and so forth. 



software 



system 



user 



word 



A set of computer programs including the operating system 
and user programs, as opposed to hardware. 

The total 1100 Series hardware/software complex comprising 
an integrated information processing installation. 

An individual or organization that consumes services 
provided by the system. 



A sequence 
capable of 
(a word is 
Systems). 



of bits or characters treated as a unit and 
being stored in a single main storage location 
represented by 36 bits for the 1100 Series 



Hardware Definitions 



ACU 



applica- 
tion 



Availability Control Unit. A device used i n 11 08- type 
Systems to isolate particular system components for main- 
tenance or system partitioning. The ACU, in certain 
operating modes, can initiate autorecovery. 

The total installation hardware configuration or a subset 
resulting from partitioning that configuration via hard- 
ware or software. 



auxiliary Supplemental storage, as opposed to main storage.' It is 
storage not directly addressable by CPU(s) and is "accessible only 
through an 1/0 interface. It includes magnetic tapes, 
flying- head magnetic drum, FASTRAND drum, disk, or 
unitized channel storage. 



break- 
point 

CAU 



central 
group 

central 
site 

channel 



A feature whereby the CPU can be stopped or interrupted 
when a particular main storage address is read, written, 
or executed as an instruction. 

Command/Arithmetic Unit. It is the 1110, 1100/40 equivalent 
of the instruction processing portion of a CPU. A CAU does 
not contain an input/output section, as does a CPU. There- 
fore, it must operate in conjunction with an I0AU in order 
to access peripheral' subsystems. 

The CPUs, CAUs, IOAUs, IOUs, ACUs, SPUs, STUs, and consoles. 



The central group, main storage, and attached onsite 
peripheral equipment in a particular application. 

A data path for transfer of information between the central 
group and 1/0 devices. 



131 



CPU The Central Processor Unit component on 1108 and 1100/80 

Systems which executes all control and arithmetic functions. 
The 1108 System CPU contains an input/output section for 
access to peripheral devices. 

CRT Cathode-ray tube display. A television-like device that 
presents data in visual form. 

dual Two separate data paths for transfer of information between 
channel the central group and a subsystem. The sub system control 
unit must have dual channel capability. 

IOAU The IOAU controls all transfers of data between the peripheral 
devices and primary and extended storage. Transfers are 
initiated by CAU under program control. 

IOU The IOU controls all transfers of data between the peripheral 
devices and primary and extended storage. Transfers are 
initiated by CAU under program control . 

interface The logical path between two connected nodes. 

interlock A condition in which a peripheral unit is unable to perform 
an executable command until the condition is removed by the 
operator. 

layered A hardware architecture wherein different parts of main 
storage storage have different performance characteristics. On the 

1110, and 1100/40, this refers to the fact that main storage 

consists of primary and extended storage. 

line-id Identification of the communications line -to which one or 
more remote terminals are attached. Line- id is a unique 
identifier of one to six alphanumeric characters assigned 
by the installation. 

main The general-purpose high speed magnetic core, semiconductor 
storage or plated wire (1110 only) storage of the system directly 

addressable by the CPU, CAU, and IOAU/ IOU and serving 

principally to contain executing programs. 

mass Auxiliary storage which has random access capability, as 
storage opposed to magnetic tape, for example. Includes any type 

of flying-head magnetic drum, FASTRAND drum units, disk, 

and unitized channel' storage. 

word-addressable Mass storage which is capable of being 
mass storage accessed in units of single words in- 

cluding any flying-head magnetic drum, 
and unitized channel storage. Word 
addressable mass storage may be simu- 
lated on disk. 



132 



FASTRAND- formatted Mass storage which is accessible in units 
mass storage of 28 words Cone sector). This may be on 

actual FASTRAND drum hardware, or may be 
simulated on other mass storage devices. 
The term FASTRAND in this manual refers 
to the format, not the hardware device, 
unless otherwise stated. This is the 
most common mass storage format. 

fixed mass storage Drum, unitized channel storage, FASTRAND 

drum units, and disk units declared to 
be fixed during the boot of the system. 
This storage is considered to be perma- 
nent (online). 

MP Multiprocessor. An application having two or more CPUs or 
CAUs. 

network All the nodes and interfaces in a system. 

node A system component. 

offline A condition in which hardware components are not under direct 
control of the operating system. 

online A condition in which hardware components are under direct 
control of the operating system. 

P- - Program address register. A CPU control register which 
register contains the absolute main storage address of the next 

instruction to be executed. See Appendix A for numeric 

conversions. 

peripheral Hardware that is distinct from the CPU, IOAU/IOU and main 
equipment storage, and which provides the system with increased 
storage capacity, or with I/O capability. 

remote Data terminal equipment that is time, space, or electrical! 
site distant from a central site, and capable of information 
exchange with the central site via communications lines. 

site-id Identification of a remote terminal. Site-id is a unique 
identifier of six alphanumeric characters assigned by the 
installation to a terminal or group of terminals. 

SPU System Partitioning Unit. A device used in the 1110 System 
which permits offline maintenance of units, enables the 
operator to logically partition the system into two or three 
independent systems, and can initiate a recovery sequence 
in the event of failure. 

STU System Transition Unit. It contains the controls and 
indicators for partitioning the SPERRY UNIVAC 1100/80 
Systems into two independent systems. It also provides an 
automatic recovery feature and system power control . 

133 



subsystem One or more peripheral units of the same type, plus a 
control unit which is connected to an available I/O 
channel. (.Can be a dual subsystem). 

symbiont Relatively slow-speed devices, such as card readers, card 
device "punches, and printers are controlled by symbionts and are 
used to provide direct input to and output from the system. 

system The hardward units of a system. They include CPUs, lOUs, 
conponent CAUs, IOAUs, primary storage, extended storage, control 
units, and devices and peripheral subsystems. 



system 

drjm/ 

dfsk 



TTY 



The mass storage unit to which the Executive is loaded. 
The system drum/disk is usually unit zero of the specified 
subsystem. The subsytem of the system drum/disk is 
specified during system's generation. This specification 
may be modified by the operator during tape bootstraps. 

Teletypewriter equipment involving keyboard, printer, 
and sending and receiving equipment. Used primarily as 
a demand processing terminal. 



unitized 

channel 

storage 


Main storage which is treated as and accessed by 
peripheral I/O hardware. 


UP 


Unit processor. An application having a single CPU, 
or CAU/IOAU. 


Software 


Definitions 



CPU/IOU, 



backlog The collection of runs which has been entered into the system 
and are held for facilities availability or unit directed 
time start. Backlog resides on mass storage. 

batch A mode in which runs are processed without any basic requi re- 
process- ment for interactive manual data or controlled input during 
ing processing. 

break- The division of symbiont-defined files into parts such that 
point the output of completed parts may be initiated prior to run 
completion. This procedure allows more efficient utilization 
of printers and punches when large symbiont output files are 
involved. 

check- Saves the run at a particular point in time for the purpose 
point of subsequent restart in case of error or interruption. 

deadline A batch run which is given certain schedule priorities to 
run attempt run completion by a prescheduled time. 



134 



demand 
process- 
ing 

file 



A mode in which run processing is basically dependent on 
manual interaction (.typically from a remote terminal) 

"time-sharing". 



during processing. Commonly known as 



.An organized collection of data, treated as a unit, and 
stored in such a manner as to faciliata the retrieval of 
each individual data item. Files are retained on 
auxiliary storage devices. 

catalogued file A file known to and retained by the 

Executive for a period of time not 
necessarily related to the life of a 
particular run, and retrievable by 
runs other than the run which origi- 
nally created the file. In some cases, 
a catalogued file may be accessed 
simultaneously by two or more runs. 

A transient file created by, accessible 
to, and existing within the life of a 
single run (as opoosed to catalogued 
file). 

logical The name associated with a system component. The logical 
name name is not required to connote the system component with 
which it is associated. 

real time A mode of operation in which the system's response to input 
process- is sufficiently fast to influence the operation being con- 
ing trolled. In the real time mode the program generally has 

exclusive use of a CPU/CAU. Generally, real time processing 
is under the influence of independent inputs from one or 
more communications devices. The real time mode may be 
entered from either batch or demand mode. 



temporary file 



restart 



run 



run- id 



swapping 



Resumption of processing a run from a checkpoint rather 
than from the beginning of the run. 

A group of tasks prescribed as a unit of work for the system. 
A @RUN control statement must be the first card or image of 
a run. A @FIN control statement is the last image. 

Identifies a run to the Executive. Run- id may consist of one 
to six alphanumeric characters and is specified on the @RUN 
control statement. If the specified run duplicates a run- id 
already in the system, the Executive modifies the newly sub- 
mitted run- id to make it unique. When the run- id is modified, 
both the original and the modified run-ids are output to the 
operator console. 

The 1100 Series Operating System's method of moving low 
priority runs from main storage to mass storage in order to 
provide space to load higher priority runs into main storage 
for execution. 



135 



symbiont A complex of Executive routines providing the user interface 
with symbiont devices. Symbionts buffer the output so that 
symbiont devices can handle the high speed output which the 
cemtral processor provides. This allows system processing to 
proceed at the higher internal and mass storage speeds rather 
'than at the relatively slow speed of symbiont devices . 

TSS Terminal Security System 

System Definitions 

bootstrap Act of loading (.booting) the Executive into main storage 
along with certain other initialization functions which 
vary depending on the type of bootstrap performed. Boot- 
strap is used synonymously with boot. 

initial bootstrap The method wherein the operating sy stem 

is read from the boot tape and copied onto 
mass storage devices. At the conclusion 
of the initialization, the Executive 
control routines, called the resident 
Executive, are read into main storage and 
are given control . 

recovery bootstrap The method wherein the Executive control 

routines are read from tape, disk, or 
drum and copied into main storage. 

autorecovery A recovery bootstrap of the system taken 

when a system malfunction or error is 
detected. The recovery may be system 
initialed (programmed recovery) or ACuV 
SPU/STU initiated. Operator intervention 
is not needed for either type. 

panic The process of documenting portions of main and mass storage 
dump for future analysis. Panic dumps are usually initiated by 
the operator or the Executive following a system error. 

system The process of tailoring the operating system to the parti - 
genera- cular hardware configuration and software requirements of a 
tion site. The end result of a system generation is a tape that 
contains a copy of the operating system in a form suitable 
for loading into the computer systam (i.e., a boot tape). 

zero stop A CPU/CAU stop initiated by the Executive due to either 
software or hardware detected faults. 

COMMUNICATION LINKS / 

The transmission and reception of data to and from a computer 
require a highly reliable electronic conversion process in most instances 
In general, data are generated and processed by both terminals and com- 
puters in coded formats utilizing patterns of binary bits. Transmission 



136 



of data over communication Tines requires a conversion of data from an 
electromechanical or magnetic storage format to electrical communication 
signals . These signals represent tones that are audible only when used 
to drive a suitable speaker-like or diaphragm device such as a telephone 
receiver. On receipt, the signals or tones are reconverted to equiva- 
lent electrical energy to rerecord the data mechanically or magnetically. 

The devices that perform this conversion process at both the 
sending and receiving ends of a communication line are known as either 
modems or Data Sets. (The word "modem" is an acronym for the function 
"modulate-demodulate." Modulation is the conversion of impulses to 
tones; demodulation is the reverse) . Data Sets are a specific type 
of modem installed by Bell System companies. The modem, in effect, is 
the telephone station through which a terminal talks to the timesharing 
computer. In most cases, Data Sets include telephone instruments and 
dials. 

The actual connection of terminals to modems is accomplished in 
either of two ways: 

1. The terminal can be "hard-wired" to the modem. This 
indicates that the wiring of the terminal is connected 
directly into the transmitter/ receiver unit. 

2. The modem can incorporate an audio coupler . With this 
approach, the connection is established between the 
terminal location and the computer on an ordinary voice- 
grade dial telephone. The telephone handset is inserted 
into the audio coupler of the modem, which then generates 
or reads tones into or from the telephone instrument. 

The hard-wire installation is more reliable, of higher quality, 
and of greater permanence. However, this approach requires profes- 
sional installation, represents a longer-term commitment, and is 
less flexible. 

By comparison, audio coupling is more subject to line interference 
but far more flexible. With this technique, timesharing service can 
be established or discontinued at any point where the user has a tele- 
phone instrument. 

Timesharing transmissions can be carried over many different 
kinds of communication lines. In general, line costs are directly 
related to the transmission capacity and length of a given line . 

The least expensive, lowest-capacity transmission line is known 
as a half-duplex circuit. This is simply a circuit with two wires - 
one signal line and a return, or ground - between two points. With 
a half-duplex or two-wire circuit, data can be transmitted in only 
one direction at a time. Thus a terminal cannot be receiving data 
from the computer while the operator is sending data. This type of 
communication link has been used primarily for telegraphic service. 

The next step up is to use a four-wire, or full-duplex, circuit . 
This is the tyoe of connection normally established for telephone 

137 



conversions . Most timesharing services today use full -duplex circuits. 
These can be acquired either through dial service or on a leased-li.ne 
basis. (With leasad-lina service, a full-duplex ine is rented on a~ 
regular basis from telephone common carriers.) In general , a full- 
duplex line has the capacity to transmit or receive at a rate of up 
to 2400 baud, or bits of data oer second. This is equivalent to 
approximately 2^0 characters per second . 

Consideration of this line capacity gives further dimension to 
earlier discussions of terminal speed and automated transmission from 
off-line storage media. Recorded data can be transmitted at speeds 
of up to 240 characters per second. However, even under automatic 
operation, printing terminals are limited to 30 characters oer second- 
and a typist entering data directly from a keyboard is effectively 
limited to seven or eiaht characters per second . 

Where data transmission requirements are greater, additional lines 
can be added. In general , communication lines with capacities greater 
than full -duplex are known as broadband service . Transmission capa- 
b ili ties are directly proportional to the lines available. Thus four 
lines would make a transmission rata of 4800 baud available, eight 
lines would carry 9600 baud, and so on. Services regularly available 
from telephone carriers extend to 32 lines. However, users of time- 
sharing utility services will rarely require or encounter services 
involving more than full-duplex lines. 

In some cases, however, timesharing utilities do use a technique 
known as multiplexing to concentrate transmission from a number of 
users over the same telephone lines. Multiplexors are satellite 
communication processors. (Minicomputers are often used for multi- 
plexing.) A large number of timesharing users, sometimes as many as 
132, can be linked to a single multiplexing point. ..Their trans- 
missions are then carried from the multiplexor to the central computer 
over either full-duplex or broadband lines. Typically, a multiplexor 
will be set up in a city remote from the central computer . For 
example, many timesharing companies operate computers in New York. 
These organizations then establish multiplexing points in major cities 
such as Chicago and Los Angeles, where users can link into the 
national timesharing network through local telephone calls. 



•U.S. GOVERNMENT PRINTING OFFICE : 19800-328-231/6531 



138 




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FEDERALLY COORDINATED PROGRAM (FCP) OF HIGHWAY 
RESEARCH AND DEVELOPMENT 



The Offices of Research and Development (R&D) of 
the Federal Highway Administration (FHWA) are 
responsible for a broad program of staff and contract 
research and development and a Federal-aid 
program, conducted by or through the State highway 
transportation agencies, that includes the Highway 
Planning and Research (HP&R) program and the 
National Cooperative Highway Research Program 
(NCHRP) managed by the Transportation Research 
Board. The FCP is a carefully selected group of proj- 
ects that uses research and development resources to 
obtain timely solutions to urgent national highway 
engineering problems.* 

The diagonal double stripe on the cover of this report 
represents a highway and is color-coded to identify 
the FCP category that the report falls under. A red 
stripe is used for category 1, dark blue for category 2, 
light blue for category 3, brown for category 4, gray 
for category 5, green for categories 6 and 7, and an 
orange stripe identifies category 0. 

FCP Category Descriptions 

1. Improved Highway Design and Operation 
for Safety 

Safety R&D addresses problems associated with 
the responsibilities of the FHWA under the 
Highway Safety Act and includes investigation of 
appropriate design standards, roadside hardware, 
signing, and physical and scientific data for the 
formulation of improved safety regulations. 

2. Reduction of Traffic Congestion, and 
Improved Operational Efficiency 

Traffic R&D is concerned with increasing the 
operational efficiency of existing highways by 
advancing technology, by improving designs for 
existing as well as new facilities, and by balancing 
the demand-capacity relationship through traffic 
management techniques such as bus and carpool 
preferential treatment, motorist information, and 
rerouting of traffic. 

3. Environmental Considerations in Highway 
Design, Location, Construction, and Opera- 
tion 

Environmental R&D is directed toward identify- 
ing and evaluating highway elements that affect 

* The complete seven-volume official statement of the FCP is available from 
the National Technical Information Service, Springfield, Va. 22161. Single 
copies of the introductory volume are available without charge from Program 
Analysis (HRD-3), Offices of Research and Development, Federal Highway 
Administration, Washington, D.C. 20590. 



the quality of the human environment. The goals 
are reduction of adverse highway and traffic 
impacts, and protection and enhancement of the 
environment. 

4. Improved Materials Utilization and 
Durability 

Materials R&D is concerned with expanding the 
knowledge and technology of materials properties, 
using available natural materials, improving struc- 
tural foundation materials, recycling highway 
materials, converting industrial wastes into useful 
highway products, developing extender or 
substitute materials for those in short supply, and 
developing more rapid and reliable testing 
procedures. The goals are lower highway con- 
struction costs and extended maintenance-free 
operation. 

5. Improved Design to Reduce Costs, Extend 
Life Expectancy, and Insure Structural 
Safety 

Structural R&D is concerned with furthering the 
latest technological advances in structural and 
hydraulic designs, fabrication processes, and 
construction techniques to provide safe, efficient 
highways at reasonable costs. 

6. Improved Technology for Highway 
Construction 

This category is concerned with the research, 
development, and implementation of highway 
construction technology to increase productivity, 
reduce energy consumption, conserve dwindling 
resources, and reduce costs while improving the 
quality and methods of construction. 

7. Improved Technology for Highway 
Maintenance 

This category addresses problems in preserving 
the Nation's highways and includes activities in 
physical maintenance, traffic services, manage- 
ment, and equipment. The goal is to maximize 
operational efficiency and safety to the traveling 
public while conserving resources. 

0. Other New Studies 

This category, not included in the seven-volume 
official statement of the FCP, is concerned with 
HP&R and NCHRP studies not specifically related 
to FCP projects. These studies involve R&D 
support of other FHWA program office research. 



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